truth table: test_truth_table_tests

I want to write a program that makes the tests in test_truth_table.py pass without looking at them

requirements

continue the project

  • Make sure you are in the pumping_python folder with pwd in the terminal

    pwd

    if the terminal does not show

    .../pumping_python

    change directory to the pumping_python folder

  • Once in pumping_python, change directory to the project

    cd truth_table

    the terminal shows

    .../pumping_python/truth_table

  • I run the tests with pytest-watcher

    uv run pytest-watcher . --now

    the terminal is my friend, and shows

    rootdir: .../pumping_python/truth_table
configfile: pyproject.toml
collected 20 items

tests/test_binary.py ....................                     [ 80%]
tests/test_nullary_unary.py ....                              [100%]

======================== 20 passed in G.HIs ========================

RED: make it fail

  • I open truth_table.py from the src folder

  • I delete everything in truth_table.py, the terminal is my friend, and shows 20 failures, I start with the last one

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_negation'

    because …

    Can you make the tests pass without looking at how I solve it below? You can come back to compare solutions when you are done.

GREEN: make it pass

  • I add the name to truth_table.py

    1logical_negation

    the terminal is my friend, and shows NameError

    NameError: name 'logical_negation' is not defined

  • I point it to None to define it

    1logical_negation = None

    the terminal is my friend, and shows TypeError

    TypeError: 'NoneType' object is not callable

    because I cannot call None like a function.

  • I make it a function

    1# logical_negation
2def logical_negation():
3    return None

    the terminal is my friend, and shows TypeError

    TypeError: logical_negation() takes
           0 positional arguments but 1 was given

  • I add a name in parentheses

    1# logical_negation
2# def logical_negation():
3def logical_negation(something):
4    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

    the assertion expects True.

  • I change None in the return statement to give the test what it wants

    1# logical_negation
2# def logical_negation():
3def logical_negation(something):
4    # return None
5    return True

    the terminal shows AssertionError

    AssertionError: True is not false

    the assertion expects False and the function returns True.

  • I change the return statement

    1# logical_negation
2# def logical_negation():
3def logical_negation(something):
4    # return None
5    # return True
6    return False

    the terminal is my friend, and shows AssertionError

    AssertionError: False is not true

  • I change the return statement to see the difference between the input and what the assertion expects, remember the identity_function?

    1# logical_negation
2# def logical_negation():
3def logical_negation(something):
4    # return None
5    # return True
6    # return False
7    return something

    the terminal is my friend, and shows AssertionError

    AssertionError: True is not false

  • I use not in the return statement

    1# logical_negation
2# def logical_negation():
3def logical_negation(something):
4    # return None
5    # return True
6    # return False
7    # return something
8    return not something

    the terminal shows 19 failed, 1 passed, progress! It also shows AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_identity'

  • I add a function for it

     1# logical_negation
 2# def logical_negation():
 3def logical_negation(something):
 4    # return None
 5    # return True
 6    # return False
 7    # return something
 8    return not something
 9
10
11def logical_identity():
12    return None

    the terminal is my friend, and shows TypeError

    TypeError: logical_identity() takes
           0 positional arguments but 1 was given

  • I add a name in parentheses

    11# def logical_identity():
12def logical_identity(something):
13    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

  • I change the return statement for logical_identity to give the test what it wants

    11# def logical_identity():
12def logical_identity(something):
13    # return None
14    return True

    the terminal is my friend, and shows AssertionError

    AssertionError: True is not false

    the assertion expects False and the function returns True.

  • I change the return statement

    11# def logical_identity():
12def logical_identity(something):
13    # return None
14    # return True
15    return False

    the terminal is my friend, and shows AssertionError

    AssertionError: False is not true

    the function returned

  • I change the return statement to see the difference between the input and what the assertion expects

    11# def logical_identity():
12def logical_identity(something):
13    # return None
14    # return True
15    # return False
16    return something

    the terminal shows 18 failed, 2 passed, more progress! It also shows AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_true'

  • I add the function

    11# def logical_identity():
12def logical_identity(something):
13    # return None
14    # return True
15    # return False
16    return something
17
18
19def logical_true():
20    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

  • I change the return statement for logical_true to give the test what it wants

    19def logical_true():
20    # return None
21    return True

    17 failed, 3 passed. That was simple. the terminal is my friend, and shows AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_false'.
                Did you mean: 'logical_true'?

  • I add the function

    19def logical_true():
20    # return None
21    return True
22
23
24def logical_false():
25    return None

    the terminal shows 16 failed, 4 passed, simple again. I am getting it. The terminal also shows AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'tautology'

  • I add the function

    24def logical_false():
25    return None
26
27
28def tautology():
29    return None

    the terminal is my friend, and shows TypeError

    TypeError: tautology() takes
           0 positional arguments but 2 were given

  • I add two names in parentheses for the function to take input arguments

    28# def tautology():
29def tautology(first, second):
30    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

  • I change None to True in the return statement

    28# def tautology():
29def tautology(first, second):
30    # return None
31    return True

    the terminal shows 15 failed, 5 passed, Yes! It also shows AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'project_second'

  • I add the function

    28# def tautology():
29def tautology(first, second):
30    # return None
31    return True
32
33
34def project_second():
35    return None

    the terminal is my friend, and shows TypeError

    TypeError: project_second() takes
           0 positional arguments but 2 were given

  • I add two names in parentheses for the function to take input arguments

    34# def project_second():
35def project_second(first, second):
36    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

  • I change the return statement to give the test what it wants

    34# def project_second():
35def project_second(first, second):
36    # return None
37    return True

    the terminal is my friend, and shows AssertionError

    AssertionError: True is not false

    the assertion expects False and the function returns True.

  • I change the return statement

    34# def project_second():
35def project_second(first, second):
36    # return None
37    # return True
38    return False

    the terminal is my friend, and shows AssertionError

    AssertionError: False is not true

    the function returned

  • I change the return statement to see the difference between the input and what the assertion expects

    34# def project_second():
35def project_second(first, second):
36    # return None
37    # return True
38    # return False
39    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

    second is False and is equal to the expectation of the assertion.

  • I remove first from the return statement since second is False

    34# def project_second():
35def project_second(first, second):
36    # return None
37    # return True
38    # return False
39    # return first, second
40    return second

    the terminal shows 14 failed, 6 passed, and AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'project_first'

  • I add a function for it

    34# def project_second():
35def project_second(first, second):
36    # return None
37    # return True
38    # return False
39    # return first, second
40    return second
41
42
43def project_first():
44    return None

    the terminal is my friend, and shows TypeError

    TypeError: project_first() takes
           0 positional arguments but 2 were given

    okay, I have seen this before.

  • I add 2 names in the parentheses

    43# def project_first():
44def project_first(first, second):
45    return None

    the terminal is my friend, and shows AssertionError

    AssertionError: None is not true

  • I change the return statement to give the test what it wants

    43# def project_first():
44def project_first(first, second):
45    # return None
46    return True

    the terminal is my friend, and shows AssertionError

    AssertionError: True is not false

    the assertion expects False and the function returns True.

  • I change the return statement

    43# def project_first():
44def project_first(first, second):
45    # return None
46    # return True
47    return False

    the terminal is my friend, and shows AssertionError

    AssertionError: False is not true

    the function returned

  • I change the return statement to see the difference between the input and what the assertion expects

    43# def project_first():
44def project_first(first, second):
45    # return None
46    # return True
47    # return False
48    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

    second is True and is equal to the expectation of the assertion.

  • I remove second from the return statement since first is False

    43# def project_first():
44def project_first(first, second):
45    # return None
46    # return True
47    # return False
48    # return first, second
49    return first

    the terminal shows 13 failed, 7 passed, and AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'negate_second'

  • I add a function for negate_second with a return statement to see the difference between the input and what the assertion expects

    43# def project_first():
44def project_first(first, second):
45    # return None
46    # return True
47    # return False
48    # return first, second
49    return first
50
51
52def negate_second(first, second):
53    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement to negate_second since first and second are both not False

    52def negate_second(first, second):
53    if (first, second) == (True, True): return False
54    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add another if statement

    52def negate_second(first, second):
53    if (first, second) == (True, True): return False
54    if (first, second) == (False, True): return False
55    return first, second

    the terminal is my friend, and shows 12 failed, 8 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'negate_first'

  • I add a function for it with a return statement to see the difference between the input and what the assertion expects

    52def negate_second(first, second):
53    if (first, second) == (True, True): return False
54    if (first, second) == (False, True): return False
55    return first, second
56
57
58def negate_first(first, second):
59    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True)

  • I add an if statement since first and second are both not False

    58def negate_first(first, second):
59    if (first, second) == (True, True): return False
60    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add another if statement

    58def negate_first(first, second):
59    if (first, second) == (True, True): return False
60    if (first, second) == (True, False): return False
61    return first, second

    the terminal is my friend, and shows 11 failed, 9 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'material_non_implication'

  • I add a function for material_non_implication with a return statement to see the difference between the input and what the assertion expects

    58def negate_first(first, second):
59    if (first, second) == (True, True): return False
60    if (first, second) == (True, False): return False
61    return first, second
62
63
64def material_non_implication(first, second):
65    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement since first and second are both not False

    64def material_non_implication(first, second):
65    if (first, second) == (True, True): return False
66    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add another if statement

    64def material_non_implication(first, second):
65    if (first, second) == (True, True): return False
66    if (first, second) == (False, True): return False
67    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add an if statement for it

    64def material_non_implication(first, second):
65    if (first, second) == (True, True): return False
66    if (first, second) == (False, True): return False
67    if (first, second) == (False, False): return False
68    return first, second

    the terminal is my friend, and shows 10 failed, 10 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'material_implication'

  • I add a function for material_implication with a return statement to see the difference between the input and what the assertion expects

    64def material_non_implication(first, second):
65    if (first, second) == (True, True): return False
66    if (first, second) == (False, True): return False
67    if (first, second) == (False, False): return False
68    return first, second
69
70
71def material_implication(first, second):
72    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add an if statement for it

    71def material_implication(first, second):
72    if (first, second) == (True, False): return False
73    return first, second

    the terminal is my friend, and shows 9 failed, 11 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_nor'

  • I add a function for logical_nor

    71def material_implication(first, second):
72    if (first, second) == (True, False): return False
73    return first, second
74
75
76def logical_nor(first, second):
77    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement

    76def logical_nor(first, second):
77    if (first, second) == (True, True): return False
78    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add another if statement

    76def logical_nor(first, second):
77    if (first, second) == (True, True): return False
78    if (first, second) == (True, False): return False
79    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add an if statement

    76def logical_nor(first, second):
77    if (first, second) == (True, True): return False
78    if (first, second) == (True, False): return False
79    if (first, second) == (False, True): return False
80    return first, second

    the terminal is my friend, and shows 8 failed, 12 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_nand'.
                Did you mean: 'logical_nor'?

  • I add a function for logical_nand

    76def logical_nor(first, second):
77    if (first, second) == (True, True): return False
78    if (first, second) == (True, False): return False
79    if (first, second) == (False, True): return False
80    return first, second
81
82
83def logical_nand(first, second):
84    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement

    83def logical_nand(first, second):
84    if (first, second) == (True, True): return False
85    return first, second

    the terminal is my friend, and shows 7 failed, 13 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_equality'.
                Did you mean: 'logical_identity'?

  • I add the function

    83def logical_nand(first, second):
84    if (first, second) == (True, True): return False
85    return first, second
86
87
88def logical_equality(first, second):
89    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add an if statement

    88def logical_equality(first, second):
89    if (first, second) == (True, False): return False
90    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add another if statement

    88def logical_equality(first, second):
89    if (first, second) == (True, False): return False
90    if (first, second) == (False, True): return False
91    return first, second

    the terminal is my friend, and shows 6 failed, 14 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_disjunction'

  • I add a function for logical_disjunction

    88def logical_equality(first, second):
89    if (first, second) == (True, False): return False
90    if (first, second) == (False, True): return False
91    return first, second
92
93
94def logical_disjunction(first, second):
95    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add an if statement

    94def logical_disjunction(first, second):
95    if (first, second) == (False, False): return False
96    return first, second

    the terminal is my friend, and shows 5 failed, 15 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'logical_conjunction'.
                Did you mean: 'logical_disjunction'?

  • I add a function for logical_conjunction

     94def logical_disjunction(first, second):
 95    if (first, second) == (False, False): return False
 96    return first, second
 97
 98
 99def logical_conjunction(first, second):
100    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add an if statement

     99def logical_conjunction(first, second):
100    if (first, second) == (True, False): return False
101    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add an if statement

     99def logical_conjunction(first, second):
100    if (first, second) == (True, False): return False
101    if (first, second) == (False, True): return False
102    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add another if statement

     99def logical_conjunction(first, second):
100    if (first, second) == (True, False): return False
101    if (first, second) == (False, True): return False
102    if (first, second) == (False, False): return False
103    return first, second

    the terminal is my friend, and shows 4 failed, 16 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'exclusive_disjunction'

  • I add a function for exclusive_disjunction

     99def logical_conjunction(first, second):
100    if (first, second) == (True, False): return False
101    if (first, second) == (False, True): return False
102    if (first, second) == (False, False): return False
103    return first, second
104
105
106def exclusive_disjunction(first, second):
107    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement

    106def exclusive_disjunction(first, second):
107    if (first, second) == (True, True): return False
108    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add another if statement

    106def exclusive_disjunction(first, second):
107    if (first, second) == (True, True): return False
108    if (first, second) == (False, False): return False
109    return first, second

    the terminal is my friend, and shows 3 failed, 17 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'converse_non_implication'.
                Did you mean: 'material_non_implication'?

  • I add converse_non_implication

    106def exclusive_disjunction(first, second):
107    if (first, second) == (True, True): return False
108    if (first, second) == (False, False): return False
109    return first, second
110
111
112def converse_non_implication(first, second):
113    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement

    112def converse_non_implication(first, second):
113    if (first, second) == (True, True): return False
114    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add another if statement

    112def converse_non_implication(first, second):
113    if (first, second) == (True, True): return False
114    if (first, second) == (True, False): return False
115    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add an if statement

    112def converse_non_implication(first, second):
113    if (first, second) == (True, True): return False
114    if (first, second) == (True, False): return False
115    if (first, second) == (False, False): return False
116    return first, second

    the terminal is my friend, and shows 2 passed, 18 failed for AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'converse_implication'.
                Did you mean: 'converse_non_implication'?

  • I add converse_implication

    112def converse_non_implication(first, second):
113    if (first, second) == (True, True): return False
114    if (first, second) == (True, False): return False
115    if (first, second) == (False, False): return False
116    return first, second
117
118
119def converse_implication(first, second):
120    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add an if statement

    119def converse_implication(first, second):
120    if (first, second) == (False, True): return False
121    return first, second

    the terminal is my friend, and shows 1 failed, 19 passed with AttributeError

    AttributeError: module 'src.truth_table'
                has no attribute 'contradiction'

  • I add contradiction

    119def converse_implication(first, second):
120    if (first, second) == (False, True): return False
121    return first, second
122
123
124def contradiction(first, second):
125    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, True) is not false

  • I add an if statement

    124def contradiction(first, second):
125    if (first, second) == (True, True): return False
126    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (True, False) is not false

  • I add another if statement

    124def contradiction(first, second):
125    if (first, second) == (True, True): return False
126    if (first, second) == (True, False): return False
127    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, True) is not false

  • I add another if statement

    124def contradiction(first, second):
125    if (first, second) == (True, True): return False
126    if (first, second) == (True, False): return False
127    if (first, second) == (False, True): return False
128    return first, second

    the terminal is my friend, and shows AssertionError

    AssertionError: (False, False) is not false

  • I add an if statement

    124def contradiction(first, second):
125    if (first, second) == (True, True): return False
126    if (first, second) == (True, False): return False
127    if (first, second) == (False, True): return False
128    if (first, second) == (False, False): return False
129    return first, second

    the terminal is my friend, and shows

    ======================== 20 passed in G.HIs ========================

All the tests are passing and the world is a better place than when I started! I am going home.

REFACTOR: make it better

Wait, there is more… Since all the tests are passing, I can play with the functions I have to make them simpler and understand why my solutions work.

  • contradiction returns False in 4 cases, with 2 inputs there are only 4 cases. I add a return statement

    124def contradiction(first, second):
125    # if (first, second) == (True, True): return False
126    # if (first, second) == (True, False): return False
127    # if (first, second) == (False, True): return False
128    # if (first, second) == (False, False): return False
129    # return first, second
130    return False

    the test is still green.

  • I remove the commented lines from contradiction

    124def contradiction(first, second):
125    return False

  • converse_implication returns False in only one case. I write out the if statement for that case, to make it clearer

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    if first == False and second == True:
122        return False
123    return first, second

    still green.

  • I change the statement with not and True

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    if not first == True and second == True:
123        return False
124    return first, second

    green.

  • I remove == True

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    # if not first == True and second == True:
123    if not first and second:
124        return False
125    return first, second

    still green.

  • I add a return statement because if something: return False can be written as return not (something)

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    # if not first == True and second == True:
123    # if not first and second:
124    #     return False
125    # return first, second
126    return not (not first and second)

    the test is still green.

  • I “multiply not” by the things in the parentheses

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    # if not first == True and second == True:
123    # if not first and second:
124    #     return False
125    # return first, second
126    # return not (not first and second)
127    return (not not first) (not and) (not second)

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I change not and to or

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    # if not first == True and second == True:
123    # if not first and second:
124    #     return False
125    # return first, second
126    # return not (not first and second)
127    # return (not not first) (not and) (not second)
128    return (not not first) or (not second)

    the test is green again.

  • I remove not not because two nots make a right?

    119def converse_implication(first, second):
120    # if (first, second) == (False, True): return False
121    # if first == False and second == True:
122    # if not first == True and second == True:
123    # if not first and second:
124    #     return False
125    # return first, second
126    # return not (not first and second)
127    # return (not not first) (not and) (not second)
128    # return (not not first) or (not second)
129    return first or not second

  • I remove the commented lines

    119def converse_implication(first, second):
120    return first or not second
121
122
123def contradiction(first, second):
124    return False

  • I add an if statement for the only case that returns True in converse_non_implication

    112def converse_non_implication(first, second):
113    # if (first, second) == (True, True): return False
114    # if (first, second) == (True, False): return False
115    # if (first, second) == (False, False): return False
116    # return first, second
117    if first == False and second == True:
118        return True
119    else:
120        return False

    the test is still green.

  • I change if first == False to terms of True

    112def converse_non_implication(first, second):
113    # if (first, second) == (True, True): return False
114    # if (first, second) == (True, False): return False
115    # if (first, second) == (False, False): return False
116    # return first, second
117    # if first == False and second == True:
118    if not first == True and second == True:
119        return True
120    else:
121        return False

    green.

  • I remove == True

    112def converse_non_implication(first, second):
113    # if (first, second) == (True, True): return False
114    # if (first, second) == (True, False): return False
115    # if (first, second) == (False, False): return False
116    # return first, second
117    # if first == False and second == True:
118    # if not first == True and second == True:
119    if not first and second:
120        return True
121    else:
122        return False

    still green.

  • I add a return statement because if something: return True can be written as return something since something is grouped as True

    112def converse_non_implication(first, second):
113    # if (first, second) == (True, True): return False
114    # if (first, second) == (True, False): return False
115    # if (first, second) == (False, False): return False
116    # return first, second
117    # if first == False and second == True:
118    # if not first == True and second == True:
119    # if not first and second:
120    #     return True
121    # else:
122    #     return False
123    return not first and second

    the test is still green.

  • I remove the commented lines

    112def converse_non_implication(first, second):
113    return not first and second
114
115
116def converse_implication(first, second):
117    return first or not second
118
119
120def contradiction(first, second):
121    return False

  • I make the if statements in exclusive_disjunction simpler

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    if first == True and second == True:
111        return False
112    if first == False and second == False:
113        return False
114    return True

    the test is still green.

  • I change the new second if statement with not and True

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    if first == True and second == True:
111        return False
112    # if first == False and second == False:
113    if not first == True and not second == True:
114        return False
115    return True

    still green.

  • I remove == True

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    if first and second:
112        return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    if not first and not second:
116        return False
117    return True

    green.

  • I write everything in the second if statement with not because it happens two times in the line, I might as well make it three

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    if first and second:
112        return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    # if not first and not second:
116    if (not first) (not or) (not second):
117        return False
118    return True

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I factor out the nots

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    if first and second:
112        return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    # if not first and not second:
116    # if (not first) (not or) (not second):
117    if not (first or second):
118        return False
119    return True

    the test is green .

  • I put the two if statements together as one

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    # if first and second:
112    #     return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    # if not first and not second:
116    # if (not first) (not or) (not second):
117    # if not (first or second):
118    if (
119        (first and second)
120        or
121        (not (first or second))
122    ):
123        return False
124    return True

    the test is still green.

  • I add a return statement because if something: return False can be written as return not (something)

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    # if first and second:
112    #     return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    # if not first and not second:
116    # if (not first) (not or) (not second):
117    # if not (first or second):
118    # if (
119    #     (first and second)
120    #     or
121    #     (not (first or second))
122    # ):
123    #     return False
124    # return True
125    return not (
126        (first and second)
127        or
128        (not (first or second))
129    )

    still green.

  • I “multiply” not by everything in the parentheses since it happens two times in the line

    106def exclusive_disjunction(first, second):
107    # if (first, second) == (True, True): return False
108    # if (first, second) == (False, False): return False
109    # return first, second
110    # if first == True and second == True:
111    # if first and second:
112    #     return False
113    # if first == False and second == False:
114    # if not first == True and not second == True:
115    # if not first and not second:
116    # if (not first) (not or) (not second):
117    # if not (first or second):
118    # if (
119    #     (first and second)
120    #     or
121    #     (not (first or second))
122    # ):
123    #     return False
124    # return True
125    # return not (
126    #     (first and second)
127    #     or
128    #     (not (first or second))
129    # )
130    return (
131        (not (first and second))
132        (not or)
133        (not (not (first or second)))
134    )

    the terminal shows SyntaxError

    SyntaxError: invalid syntax

  • I change not or to and

    130    return (
131        (not (first and second))
132        # (not or)
133        and
134        (not (not (first or second)))
135    )

    the test is green again.

  • I remove not not because “the negation of a negation is …”

    130    return (
131        (not (first and second))
132        # (not or)
133        and
134        # (not (not (first or second)))
135        (first or second)
136    )

    green.

  • I remove the commented lines from exclusive_disjunction

    106def exclusive_disjunction(first, second):
107    return (not (first and second)) and (first or second)
108
109
110def converse_non_implication(first, second):
111    return not first and second
112
113
114def converse_implication(first, second):
115    return first or not second
116
117
118def contradiction(first, second):
119    return False

  • logical_conjunction has only one case that returns True. I add an if statement for it

     99def logical_conjunction(first, second):
100    # if (first, second) == (True, False): return False
101    # if (first, second) == (False, True): return False
102    # if (first, second) == (False, False): return False
103    # return first, second
104    if first == True and second == True:
105        return True
106    else:
107        return False

    the test is still green.

  • I remove == True

     99def logical_conjunction(first, second):
100    # if (first, second) == (True, False): return False
101    # if (first, second) == (False, True): return False
102    # if (first, second) == (False, False): return False
103    # return first, second
104    # if first == True and second == True:
105    if first and second:
106        return True
107    else:
108        return False

    still green.

  • I add a return statement because if something: return True can be written as return something since something is grouped as True

     99def logical_conjunction(first, second):
100    # if (first, second) == (True, False): return False
101    # if (first, second) == (False, True): return False
102    # if (first, second) == (False, False): return False
103    # return first, second
104    # if first == True and second == True:
105    # if first and second:
106    #     return True
107    # else:
108    #     return False
109    return first and second

    green.

  • I remove the commented lines from logical_conjunction

     99def logical_conjunction(first, second):
100    return first and second
101
102
103def exclusive_disjunction(first, second):
104    return (not (first and second)) and (first or second)

  • logical_disjunction has only one case that returns False, I break up the if statement

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    if first == False and second == False:
 98        return False
 99    else:
100        return True

    the test is still green.

  • I then change the if statement with not and True

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    if not first == True and not second == True:
 99        return False
100    else:
101        return True

    still green.

  • I remove == True

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    # if not first == True and not second == True:
 99    if not first and not second:
100        return False
101    else:
102        return True

    green.

  • I change the statement with not since it happens two times

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    # if not first == True and not second == True:
 99    # if not first and not second:
100    if (not first) (not or) (not second):
101        return False
102    else:
103        return True

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I factor out not

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    # if not first == True and not second == True:
 99    # if not first and not second:
100    # if (not first) (not or) (not second):
101    if not (first or second):
102        return False
103    else:
104        return True

    the test is green again.

  • I add a return statement for the opposite of the if statement because if something: return False can be written as return not (something)

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    # if not first == True and not second == True:
 99    # if not first and not second:
100    # if (not first) (not or) (not second):
101    # if not (first or second):
102    #     return False
103    # else:
104    #     return True
105    return not (not (first or second))

    still green.

  • I remove not not

     94def logical_disjunction(first, second):
 95    # if (first, second) == (False, False): return False
 96    # return first, second
 97    # if first == False and second == False:
 98    # if not first == True and not second == True:
 99    # if not first and not second:
100    # if (not first) (not or) (not second):
101    # if not (first or second):
102    #     return False
103    # else:
104    #     return True
105    # return not (not (first or second))
106    return first or second

    the test is still green.

  • I remove the commented lines from logical_disjunction

    94def logical_disjunction(first, second):
95    return first or second
96
97
98def logical_conjunction(first, second):
99    return first and second

  • I break up the if statements in logical_equality

    88def logical_equality(first, second):
89    # if (first, second) == (True, False): return False
90    # if (first, second) == (False, True): return False
91    # return first, second
92    if first == True and second == False:
93        return False
94    if first == False and second == True:
95        return False
96    return True

    the test is still green.

  • I change the if statements with not and True

    88def logical_equality(first, second):
89    # if (first, second) == (True, False): return False
90    # if (first, second) == (False, True): return False
91    # return first, second
92    # if first == True and second == False:
93    if first == True and not second == True:
94        return False
95    # if first == False and second == True:
96    if not first == True and second == True:
97        return False
98    return True

    still green.

  • I remove == True

     88def logical_equality(first, second):
 89    # if (first, second) == (True, False): return False
 90    # if (first, second) == (False, True): return False
 91    # return first, second
 92    # if first == True and second == False:
 93    # if first == True and not second == True:
 94    if first and not second:
 95        return False
 96    # if first == False and second == True:
 97    # if not first == True and second == True:
 98    if not first and second:
 99        return False
100    return True

    green.

  • I put the two if statements together as one

     88def logical_equality(first, second):
 89    # if (first, second) == (True, False): return False
 90    # if (first, second) == (False, True): return False
 91    # return first, second
 92    # if first == True and second == False:
 93    # if first == True and not second == True:
 94    # if first and not second:
 95    #     return False
 96    # if first == False and second == True:
 97    # if not first == True and second == True:
 98    # if not first and second:
 99    if (
100        (first and not second)
101        or
102        (not first and second)
103    ):
104        return False
105    return True

    still green.

  • I add a return statement because …

     88def logical_equality(first, second):
 89    # if (first, second) == (True, False): return False
 90    # if (first, second) == (False, True): return False
 91    # return first, second
 92    # if first == True and second == False:
 93    # if first == True and not second == True:
 94    # if first and not second:
 95    #     return False
 96    # if first == False and second == True:
 97    # if not first == True and second == True:
 98    # if not first and second:
 99    # if (
100    #     (first and not second)
101    #     or
102    #     (not first and second)
103    # ):
104    #     return False
105    # return True
106    return not (
107        (first and not second)
108        or
109        (not first and second)
110    )

    the test is still green.

  • I multiply not by all the symbols in parentheses

     88def logical_equality(first, second):
 89    # if (first, second) == (True, False): return False
 90    # if (first, second) == (False, True): return False
 91    # return first, second
 92    # if first == True and second == False:
 93    # if first == True and not second == True:
 94    # if first and not second:
 95    #     return False
 96    # if first == False and second == True:
 97    # if not first == True and second == True:
 98    # if not first and second:
 99    # if (
100    #     (first and not second)
101    #     or
102    #     (not first and second)
103    # ):
104    #     return False
105    # return True
106    # return not (
107    #     (first and not second)
108    #     or
109    #     (not first and second)
110    # )
111    return (
112        (not (first and not second))
113        (not or)
114        (not (not first and second))
115    )

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I change not or to and

    111    return (
112        (not (first and not second))
113        # (not or)
114        and
115        (not (not first and second))
116    )

    the test is green again.

  • I multiply not by the symbols in the first part of the statement

    111    return (
112        # (not (first and not second))
113        ((not first) (not and) (not not second))
114        # (not or)
115        and
116        (not (not first and second))
117    )

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I change not and to or

    111    return (
112        # (not (first and not second))
113        # ((not first) (not and) (not not second))
114        ((not first) or (not not second))
115        # (not or)
116        and
117        (not (not first and second))
118    )

    the test is green again.

  • I remove not not

    111    return (
112        # (not (first and not second))
113        # ((not first) (not and) (not not second))
114        # ((not first) or (not not second))
115        (not first or second)
116        # (not or)
117        and
118        (not (not first and second))
119    )

    still green.

  • I multiply not by the symbols in the second part of the statement

    111    return (
112        # (not (first and not second))
113        # ((not first) (not and) (not not second))
114        # ((not first) or (not not second))
115        (not first or second)
116        # (not or)
117        and
118        # (not (not first and second))
119        ((not not first) (not and) (not second))
120    )

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I change not and to or

    111    return (
112        # (not (first and not second))
113        # ((not first) (not and) (not not second))
114        # ((not first) or (not not second))
115        (not first or second)
116        # (not or)
117        and
118        # (not (not first and second))
119        # ((not not first) (not and) (not second))
120        ((not not first) or (not second))
121    )

    the test is green again.

  • I remove not not

    111    return (
112        # (not (first and not second))
113        # ((not first) (not and) (not not second))
114        # ((not first) or (not not second))
115        (not first or second)
116        # (not or)
117        and
118        # (not (not first and second))
119        # ((not not first) (not and) (not second))
120        # ((not not first) or (not second))
121        (first or not second)
122    )

    the test is still green.

  • I remove the commented lines from logical_equality

    88def logical_equality(first, second):
89    return (not first or second) and (first or not second)
90
91
92def logical_disjunction(first, second):
93    return first or second

  • I make the if statement in logical_nand simpler

    83def logical_nand(first, second):
84    # if (first, second) == (True, True): return False
85    # return first, second
86    if first == True and second == True:
87        return False
88    else:
89        return True

    the test is still green.

  • I remove == True

    83def logical_nand(first, second):
84    # if (first, second) == (True, True): return False
85    # return first, second
86    # if first == True and second == True:
87    if first and second:
88        return False
89    else:
90        return True

    still green.

  • I add a return statement because …

    83def logical_nand(first, second):
84    # if (first, second) == (True, True): return False
85    # return first, second
86    # if first == True and second == True:
87    # if first and second:
88    #     return False
89    # else:
90    #     return True
91    return not (first and second)

    green.

  • I remove the commented lines from logical_nand

    83def logical_nand(first, second):
84    return not (first and second)
85
86
87def logical_equality(first, second):
88    return (not first or second) and (first or not second)

  • logical_nor has only one case that returns True. I add an if statement for it

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    if first == False and second == False:
82        return True
83    else:
84        return False

    the test is still green.

  • I use not to write the if statement in terms of True

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    # if first == False and second == False:
82    if not first == True and not second == True:
83        return True
84    else:
85        return False

    still green.

  • I remove == True

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    # if first == False and second == False:
82    # if not first == True and not second == True:
83    if not first and not second:
84        return True
85    else:
86        return False

    green.

  • I add a return statement

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    # if first == False and second == False:
82    # if not first == True and not second == True:
83    # if not first and not second:
84    #     return True
85    # else:
86    #     return False
87    return not first and not second

    still green.

  • I write the statement with not because it happens 2 times

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    # if first == False and second == False:
82    # if not first == True and not second == True:
83    # if not first and not second:
84    #     return True
85    # else:
86    #     return False
87    # return not first and not second
88    return (not first) (not or) (not second)

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I factor out not

    76def logical_nor(first, second):
77    # if (first, second) == (True, True): return False
78    # if (first, second) == (True, False): return False
79    # if (first, second) == (False, True): return False
80    # return first, second
81    # if first == False and second == False:
82    # if not first == True and not second == True:
83    # if not first and not second:
84    #     return True
85    # else:
86    #     return False
87    # return not first and not second
88    # return (not first) (not or) (not second)
89    return not (first or second)

    the test is green again.

  • I remove the commented lines from logical_nor

    76def logical_nor(first, second):
77    return not (first or second)
78
79
80def logical_nand(first, second):
81    return not (first and second)

  • I add return statement for the if statement of material_implication because if something: return False can be written as return not (something)

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    return not ((first, second) == (True, False))

    the test is still green.

  • I break up the return statement to make it simpler

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    return not (first == True and second == False)

    still green.

  • I use not to rewrite it in terms of True

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    # return not (first == True and second == False)
76    return not (first == True and not second == True)

    green.

  • I remove == True

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    # return not (first == True and second == False)
76    # return not (first == True and not second == True)
77    return not (first and not second)

    still green.

  • I multiply not by everything in parentheses

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    # return not (first == True and second == False)
76    # return not (first == True and not second == True)
77    # return not (first and not second)
78    return (not first) (not and) (not not second)

    the terminal is my friend, and shows SyntaxError

    SyntaxError: invalid syntax

  • I change not and to or

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    # return not (first == True and second == False)
76    # return not (first == True and not second == True)
77    # return not (first and not second)
78    # return (not first) (not and) (not not second)
79    return (not first) or (not not second)

    the test is green again.

  • I remove not not

    71def material_implication(first, second):
72    # if (first, second) == (True, False): return False
73    # return first, second
74    # return not ((first, second) == (True, False))
75    # return not (first == True and second == False)
76    # return not (first == True and not second == True)
77    # return not (first and not second)
78    # return (not first) (not and) (not not second)
79    # return (not first) or (not not second)
80    return not first or second

    the test is still green.

  • I remove the commented lines from material_implication

    71def material_implication(first, second):
72    return not first or second
73
74
75def logical_nor(first, second):
76    return not (first or second)

  • material_non_implication has 3 cases that return False. I add a return statement for the case that returns True

    64def material_non_implication(first, second):
65    # if (first, second) == (True, True): return False
66    # if (first, second) == (False, True): return False
67    # if (first, second) == (False, False): return False
68    # return first, second
69    return (first, second) == (True, False)

    the test is still green.

  • I make the return statement simpler

    64def material_non_implication(first, second):
65    # if (first, second) == (True, True): return False
66    # if (first, second) == (False, True): return False
67    # if (first, second) == (False, False): return False
68    # return first, second
69    # return (first, second) == (True, False)
70    return first == True and second == False

    still green.

  • I use not to write it in terms of True

    64def material_non_implication(first, second):
65    # if (first, second) == (True, True): return False
66    # if (first, second) == (False, True): return False
67    # if (first, second) == (False, False): return False
68    # return first, second
69    # return (first, second) == (True, False)
70    # return first == True and second == False
71    return first == True and not second == True

    green.

  • I remove == True

    64def material_non_implication(first, second):
65    # if (first, second) == (True, True): return False
66    # if (first, second) == (False, True): return False
67    # if (first, second) == (False, False): return False
68    # return first, second
69    # return (first, second) == (True, False)
70    # return first == True and second == False
71    # return first == True and not second == True
72    return first and not second

    still green.

  • I remove the commented lines from material_non_implication

    64def material_non_implication(first, second):
65    return first and not second
66
67
68def material_implication(first, second):
69    return not first or second

  • first is True in the two cases where negate_first returns False, I add an if statement for them

    58def negate_first(first, second):
59    # if (first, second) == (True, True): return False
60    # if (first, second) == (True, False): return False
61    # return first, second
62    if first == True:
63        return False
64    else:
65        return True

    the test is still green.

  • I add a return statement because …

    58def negate_first(first, second):
59    # if (first, second) == (True, True): return False
60    # if (first, second) == (True, False): return False
61    # return first, second
62    # if first == True:
63    #     return False
64    # else:
65    #     return True
66    return not first == True

    still green.

  • I remove == True

    58def negate_first(first, second):
59    # if (first, second) == (True, True): return False
60    # if (first, second) == (True, False): return False
61    # return first, second
62    # if first == True:
63    #     return False
64    # else:
65    #     return True
66    # return not first == True
67    return not first

    green.

  • I remove the commented lines from negate_first

    58def negate_first(first, second):
59    return not first
60
61
62def material_non_implication(first, second):
63    return first and not second

  • second is True in the two cases where negate_second returns False. I add an if statement for them

    52def negate_second(first, second):
53    # if (first, second) == (True, True): return False
54    # if (first, second) == (False, True): return False
55    # return first, second
56    if second == True:
57        return False
58    else:
59        return True

    the test is still green.

  • I add a return statement because if something == False: can be written as return not something

    52def negate_second(first, second):
53    # if (first, second) == (True, True): return False
54    # if (first, second) == (False, True): return False
55    # return first, second
56    # if second == True:
57    #     return False
58    # else:
59    #     return True
60    return not second == True

    still green.

  • I remove == True

    52def negate_second(first, second):
53    # if (first, second) == (True, True): return False
54    # if (first, second) == (False, True): return False
55    # return first, second
56    # if second == True:
57    #     return False
58    # else:
59    #     return True
60    # return not second == True
61    return not second

    green.

  • I remove the commented lines from truth_table.py because all the other functions are already simple

     1def logical_negation(something):
 2    return not something
 3
 4
 5def logical_identity(something):
 6    return something
 7
 8
 9def logical_true():
10    return True
11
12
13def logical_false():
14    return None
15
16
17def tautology(first, second):
18    return True
19
20
21def project_second(first, second):
22    return second
23
24
25def project_first(first, second):
26    return first
27
28
29def negate_second(first, second):
30    return not second
31
32
33def negate_first(first, second):
34    return not first
35
36
37def material_non_implication(first, second):
38    return first and not second
39
40
41def material_implication(first, second):
42    return not first or second
43
44
45def logical_nor(first, second):
46    return not (first or second)
47
48
49def logical_nand(first, second):
50    return not (first and second)
51
52
53def logical_equality(first, second):
54    return (not first or second) and (first or not second)
55
56
57def logical_disjunction(first, second):
58    return first or second
59
60
61def logical_conjunction(first, second):
62    return first and second
63
64
65def exclusive_disjunction(first, second):
66    return (not (first and second)) and (first or second)
67
68
69def converse_non_implication(first, second):
70    return not first and second
71
72
73def converse_implication(first, second):
74    return first or not second
75
76
77def contradiction(first, second):
78    return False

close the project

  • I close truth_table.py

  • I click in the terminal where the tests are running

  • I use q on the keyboard to leave the tests. The terminal goes back to the command line.

  • I change directory to the parent of truth_table

    cd ..

    the terminal shows

    .../pumping_python

    I am back in the pumping_python directory

review

I ran tests using booleans which can be False or True, for the operations of the Truth Table from Mathematics

and

All the binary operations or conditions have been written with some or all of the above 3.

code from the chapter

Do you want to see all the CODE I typed for the Truth Table?

what is next?

you now know

how to make a Python test driven development environment manually * what causes AssertionError? * how to make functions * what causes AttributeError * how to pass values from tests to functions * what is None and NOT None * what is True and False in Python * how to write programs that make decisions

Would you like to test projects that use the Truth Table?

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