truth table: Binary Operations part 3

requirements

Binary Operations part 2

how to get back to the automated tests

If your tests stopped after the previous chapter, heres’s how to get back to the tests

test_exclusive_disjunction

RED: make it fail

I add a new test to test_truth_table.py

73        self.assertFalse(src.truth_table.logical_disjunction(False, False))
74
75    def test_exclusive_disjunction(self):
76        self.assertFalse(src.truth_table.exclusive_disjunction(True, True))
77
78
79# Exceptions seen

the terminal shows AttributeError

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

GREEN: make it pass

I add the function for exclusive_disjunction in truth_table.py

45def logical_disjunction(first_input, second_input):
46    return first_input or second_input
47
48
49def exclusive_disjunction(first_input, second_input):
50    return False

the test passes. exclusive_disjunction returns False when the two inputs are True

REFACTOR: make it better

  • I add the next case to test_exclusive_disjunction in test_truth_table.py

    75    def test_exclusive_disjunction(self):
76        self.assertFalse(src.truth_table.exclusive_disjunction(True, True))
77        self.assertTrue(src.truth_table.exclusive_disjunction(True, False))

    the terminal shows AssertionError

    AssertionError: False is not true

  • I add if statements to exclusive_disjunction in truth_table.py

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == True:
51        if second_input == False:
52            return True
53    return False

    the test passes

  • I change the two if statements to one if statement

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == True and second_input == False:
51    # if first_input == True:
52    #     if second_input == False:
53            return True
54    return False

    still green

  • I remove the commented line and move the return statement to the left

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == True and second_input == False:
51        return True
52    return False

    the terminal still shows green. exclusive_disjunction returns

  • I add the third case to test_exclusive_disjunction in test_truth_table.py

    75    def test_exclusive_disjunction(self):
76        self.assertFalse(src.truth_table.exclusive_disjunction(True, True))
77        self.assertTrue(src.truth_table.exclusive_disjunction(True, False))
78        self.assertTrue(src.truth_table.exclusive_disjunction(False, True))

    the terminal shows AssertionError

    AssertionError: False is not true

  • I add if statements to exclusive_disjunction in truth_table.py

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == False:
51        if second_input == True:
52            return True
53    if first_input == True and second_input == False:
54        return True
55    return False

    the test passes

  • I change the new statements to one if statement

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == False and second_input == True:
51    # if first_input == False:
52    #     if second_input == True:
53            return True
54    if first_input == True and second_input == False:
55        return True
56    return False

    still green

  • I remove the comments and move the return statement to the left

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == False and second_input == True:
51        return True
52    if first_input == True and second_input == False:
53        return True
54    return False

    the terminal still shows green. exclusive_disjunction returns

  • I add the last case to test_exclusive_disjunction in test_truth_table.py

    75    def test_exclusive_disjunction(self):
76        self.assertFalse(src.truth_table.exclusive_disjunction(True, True))
77        self.assertTrue(src.truth_table.exclusive_disjunction(True, False))
78        self.assertTrue(src.truth_table.exclusive_disjunction(False, True))
79        self.assertFalse(src.truth_table.exclusive_disjunction(False, False))
80
81
82# Exceptions seen

    the test is still green. exclusive_disjunction returns

  • I write the if statements in terms of True

    49def exclusive_disjunction(first_input, second_input):
50    if not first_input == True and second_input == True:
51    # if first_input == False and second_input == True:
52        return True
53    if first_input == True and not second_input == True:
54    # if first_input == True and second_input == False:
55        return True
56    return False

    is green the color of money?

  • I remove the commented lines and make the statements simpler with bool

    49def exclusive_disjunction(first_input, second_input):
50    if not bool(first_input) and bool(second_input):
51    # if not first_input == True and second_input == True:
52        return True
53    if bool(first_input) and not bool(second_input):
54    # if first_input == True and not second_input == True:
55        return True
56    return False

    still green

  • I remove the commented lines and make the if statements simpler

    49def exclusive_disjunction(first_input, second_input):
50    if not first_input and second_input:
51    # if not bool(first_input) and bool(second_input):
52        return True
53    if first_input and not second_input:
54    # if bool(first_input) and not bool(second_input):
55        return True
56    return False

    the test is still passing

    Tip

    I can put two if statements together with Logical Disjunction (or) when they are at the same indentation level and return the same thing. For example

    if something:
    return this
if something_else:
    return this

    can also be written as

    if something or something_else:
    return this

  • I use Logical Disjunction to put the two if statements that return True together

    49def exclusive_disjunction(first_input, second_input):
50    if (not first_input and second_input) or (first_input and not second_input):
51        return True
52    # if not first_input and second_input:
53    #     return True
54    # if first_input and not second_input:
55    #     return True
56    return False

    the test is still green

  • I remove the commented lines

    49def exclusive_disjunction(first_input, second_input):
50    if (not first_input and second_input) or (first_input and not second_input):
51        return True
52    return False

    the test is still passing

  • I use a conditional expression

    49def exclusive_disjunction(first_input, second_input):
50    return True if (not first_input and second_input) or (first_input and not second_input) else False
51    if (not first_input and second_input) or (first_input and not second_input):
52        return True
53    return False

    why is the grass greener on the other side?

  • I remove the other statements and make the ternary operator simpler

    49def exclusive_disjunction(first_input, second_input):
50    return (not first_input and second_input) or (first_input and not second_input)
51    return True if (not first_input and second_input) or (first_input and not second_input) else False

    the terminal still shows green

  • I remove the second return statement

    49def exclusive_disjunction(first_input, second_input):
50    return (not first_input and second_input) or (first_input and not second_input)

    still green

  • exclusive_disjunction returns False when first_input and second_input are the same and returns True when they are NOT. I add an if statement to show this with the equality symbol (2 equal signs together =+=)

    49def exclusive_disjunction(first_input, second_input):
50    if first_input == second_input:
51        return False
52    else:
53        return True
54    return (not first_input and second_input) or (first_input and not second_input)

    the terminal still shows green

  • I change the new if statement to a simple return statement

    49def exclusive_disjunction(first_input, second_input):
50    return not (first_input == second_input)
51    # if first_input == second_input:
52    #     return False
53    # else:
54    #     return True
55    return (not first_input and second_input) or (first_input and not second_input)

    the test is still green

  • I remove the commented lines, then use an even simpler return statement with the NOT equal symbol (exclamation mark and equal symbol !+=)

    49def exclusive_disjunction(first_input, second_input):
50    return first_input != second_input
51    return not (first_input == second_input)
52    return (not first_input and second_input) or (first_input and not second_input)

Exclusive Disjunction returns

all of the above statements mean the same thing. Would “Logical Inequality” be a better name for Exclusive Disjunction?

Exclusive Disjunction is also known as Exclusive OR or XOR which is used in many different fields

test_material_non_implication

RED: make it fail

I add another test to test_truth_table.py

79        self.assertFalse(src.truth_table.exclusive_disjunction(False, False))
80
81    def test_material_non_implication(self):
82        self.assertFalse(src.truth_table.material_non_implication(True, True))
83
84
85# Exceptions seen

the terminal shows AttributeError

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

GREEN: make it pass

I add a function for material_non_implication in truth_table.py

49def exclusive_disjunction(first_input, second_input):
50    return first_input != second_input
51    return not first_input == second_input
52    return (not first_input and second_input) or (first_input and not second_input)
53
54
55def material_non_implication(first_input, second_input):
56    return False

the test passes. material_non_implication returns False when the two inputs are True

REFACTOR: make it better

  • I add another case to test_material_non_implication in test_truth_table.py

    81    def test_material_non_implication(self):
82        self.assertFalse(src.truth_table.material_non_implication(True, True))
83        self.assertTrue(src.truth_table.material_non_implication(True, False))

    the terminal shows AssertionError

    AssertionError: False is not true

  • I add an if statement to material_non_implication in truth_table.py

    55def material_non_implication(first_input, second_input):
56    if first_input == True:
57        if second_input == False:
58            return True
59    return False

    the test passes

  • I change the two if statements to one

    55def material_non_implication(first_input, second_input):
56    if first_input == True and second_input ==False:
57    # if first_input == True:
58    #     if second_input == False:
59            return True
60    return False

    the test is still green

  • I remove the commented lines and move the new return statement to the left

    55def material_non_implication(first_input, second_input):
56    if first_input == True and second_input ==False:
57        return True
58    return False

    the test is still green. material_non_implication returns

  • I add the next case in test_truth_table.py

    81    def test_material_non_implication(self):
82        self.assertFalse(src.truth_table.material_non_implication(True, True))
83        self.assertTrue(src.truth_table.material_non_implication(True, False))
84        self.assertFalse(src.truth_table.material_non_implication(False, True))

    the test is still green. material_non_implication returns

  • I add the fourth case

    81    def test_material_non_implication(self):
82        self.assertFalse(src.truth_table.material_non_implication(True, True))
83        self.assertTrue(src.truth_table.material_non_implication(True, False))
84        self.assertFalse(src.truth_table.material_non_implication(False, True))
85        self.assertFalse(src.truth_table.material_non_implication(False, False))
86
87
88# Exceptions seen

    the terminal still shows green. material_non_implication returns

  • there is only one case where material_non_implication returns True. I write the if statement in terms of True in truth_table.py

    55def material_non_implication(first_input, second_input):
56    if first_input == True and not second_input == True:
57    # if first_input == True and second_input ==False:
58        return True
59    return False

    the test is still passing

  • I remove the commented line and change the if statement with bool

    55def material_non_implication(first_input, second_input):
56    if bool(first_input) and not bool(second_input):
57    # if first_input == True and not second_input == True:
58        return True
59    return False

    green is a primary color

  • I remove the commented line and write a simpler if statement

    55def material_non_implication(first_input, second_input):
56    if first_input and not second_input:
57    # if bool(first_input) and not bool(second_input):
58        return True
59    return False

    the test is still green

  • I remove the commented lines then add a conditional expression

    55def material_non_implication(first_input, second_input):
56    return first_input and not second_input
57    if first_input and not second_input:
58        return True
59    return False

    the test is still green

  • I remove the other statements

    55def material_non_implication(first_input, second_input):
56    return first_input and not second_input

Material NonImplication returns

test_project_first

RED: make it fail

I add a new test in test_truth_table.py

85        self.assertFalse(src.truth_table.material_non_implication(False, False))
86
87    def test_project_first(self):
88        self.assertTrue(src.truth_table.project_first(True, True))
89
90
91# Exceptions seen

the terminal shows AttributeError

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

GREEN: make it pass

I add a function definition for project_first in truth_table.py

55def material_non_implication(first_input, second_input):
56    return first_input and not second_input
57
58
59def project_first(first_input, second_input):
60    return True

the test passes. project_first returns True when the two inputs are True

REFACTOR: make it better

  • I add the second case to test_project_first in test_truth_table.py

    87    def test_project_first(self):
88        self.assertTrue(src.truth_table.project_first(True, True))
89        self.assertTrue(src.truth_table.project_first(True, False))

    the test is still green. project_first returns

  • on to the next case

    87    def test_project_first(self):
88        self.assertTrue(src.truth_table.project_first(True, True))
89        self.assertTrue(src.truth_table.project_first(True, False))
90        self.assertFalse(src.truth_table.project_first(False, True))

    the terminal shows AssertionError

    AssertionError: True is not false

  • I add if statements for this case to project_first in truth_table.py

    59def project_first(first_input, second_input):
60    if first_input == False:
61        if second_input == True:
62            return False
63    return True

    the test passes. project_first returns

  • I change the if statements to one if statement

    59def project_first(first_input, second_input):
60    if first_input == False and second_input == True:
61    # if first_input == False:
62    #     if second_input == True:
63            return False
64    return True

    the terminal still shows green

  • I remove the commented line and move the return statement to the left

    59def project_first(first_input, second_input):
60    if first_input == False and second_input == True:
61        return False
62    return True

    the test is still green

  • I add the last case to test_project_first in test_truth_table.py

    87    def test_project_first(self):
88        self.assertTrue(src.truth_table.project_first(True, True))
89        self.assertTrue(src.truth_table.project_first(True, False))
90        self.assertFalse(src.truth_table.project_first(False, True))
91        self.assertFalse(src.truth_table.project_first(False, False))
92
93
94# Exceptions seen

    the terminal shows AssertionError

    AssertionError: True is not false

  • I add if statements to project_first in truth_table.py

    59def project_first(first_input, second_input):
60    if first_input == False:
61        if second_input == False:
62            return False
63    if first_input == False and second_input == True:
64        return False
65    return True

    the test passes

  • I change the if statements to one if statement

    59def project_first(first_input, second_input):
60    if first_input == False and second_input == False:
61    # if first_input == False:
62    #     if second_input == False:
63            return False
64    if first_input == False and second_input == True:
65        return False
66    return True

    the test is still green

  • I remove the commented lines, and move the return statement to the left

    59def project_first(first_input, second_input):
60    if first_input == False and second_input == False:
61        return False
62    if first_input == False and second_input == True:
63        return False
64    return True

    the test is still green. project_first returns

  • I add a return statement to show that this function returns the same value as first_input in every case

    59def project_first(first_input, second_input):
60    return first_input
61    if first_input == False and second_input == False:
62        return False
63    if first_input == False and second_input == True:
64        return False
65    return True

    the terminal still shows green

  • I remove the other statements

    59def project_first(first_input, second_input):
60    return first_input

Project First returns the first input, it always returns

it is like Project Second which always returns the second input

test_converse_implication

RED: make it fail

I add a new test to test_truth_table.py

91        self.assertFalse(src.truth_table.project_first(False, False))
92
93    def test_converse_implication(self):
94        self.assertTrue(src.truth_table.converse_implication(True, True))
95
96
97# Exceptions seen

the terminal shows AttributeError

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

GREEN: make it pass

I add a function definition for converse_implication in truth_table.py

59def project_first(first_input, second_input):
60    return first_input
61
62
63def converse_implication(first_input, second_input):
64    return True

the test passes. converse_implication returns True when first_input and second_input are both True

REFACTOR: make it better

  • I add the second case to test_converse_implication in test_truth_table.py

    93    def test_converse_implication(self):
94        self.assertTrue(src.truth_table.converse_implication(True, True))
95        self.assertTrue(src.truth_table.converse_implication(True, False))

    the test is still green. converse_implication returns

  • time for the next case

    93    def test_converse_implication(self):
94        self.assertTrue(src.truth_table.converse_implication(True, True))
95        self.assertTrue(src.truth_table.converse_implication(True, False))
96        self.assertFalse(src.truth_table.converse_implication(False, True))

    the terminal shows AssertionError

    AssertionError: True is not false

  • I add if statements to converse_implication in truth_table.py

    63def converse_implication(first_input, second_input):
64    if first_input == False:
65        if second_input == True:
66            return False
67    return True

    the test passes

  • I change the two if statements to one if statement

    63def converse_implication(first_input, second_input):
64    if first_input == False and second_input == True:
65    # if first_input == False:
66    #     if second_input == True:
67            return False
68    return True

    the test is still green

  • I remove the commented lines and move the return statement to the left

    63def converse_implication(first_input, second_input):
64    if first_input == False and second_input == True:
65        return False
66    return True

    still green. converse_implication returns

  • I add the last case to test_converse_implication in test_truth_table.py

     93    def test_converse_implication(self):
 94        self.assertTrue(src.truth_table.converse_implication(True, True))
 95        self.assertTrue(src.truth_table.converse_implication(True, False))
 96        self.assertFalse(src.truth_table.converse_implication(False, True))
 97        self.assertTrue(src.truth_table.converse_implication(False, False))
 98
 99
100# Exceptions seen

    the terminal still shows green. converse_implication returns

  • I change the if statement in terms of True in truth_table.py

    63def converse_implication(first_input, second_input):
64    if not first_input == True and second_input == True:
65    # if first_input == False and second_input == True:
66        return False
67    return True

    the test is still green

  • I remove the commented line and use bool

    63def converse_implication(first_input, second_input):
64    if not bool(first_input) and bool(second_input):
65    # if not first_input == True and second_input == True:
66        return False
67    return True

    do you like green eggs and ham?

  • I remove the commented line and make the if statement simpler

    63def converse_implication(first_input, second_input):
64    if not first_input and second_input:
65    # if not bool(first_input) and bool(second_input):
66        return False
67    return True

    the terminal still shows green

  • I add the opposite of the if statement for the second return statement

    63def converse_implication(first_input, second_input):
64    if not first_input and second_input:
65        return False
66    if not (not first_input and second_input):
67        return True

    the test is still passing

  • I move the new if statement to the top

    63def converse_implication(first_input, second_input):
64    if not (not first_input and second_input):
65        return True
66    if not first_input and second_input:
67        return False

    green

  • I add a conditional expression

    63def converse_implication(first_input, second_input):
64    return True if not (not first_input and second_input) else False
65    if not (not first_input and second_input):
66        return True
67    if not first_input and second_input:
68        return False

    the test is still green

  • I remove the other if statements and write a simpler conditional expression

    63def converse_implication(first_input, second_input):
64    return not (not first_input and second_input)
65    return True if not (not first_input and second_input) else False

    the terminal still shows green

  • I remove the commented lines and “multiply not” by the symbols in the parentheses

    63def converse_implication(first_input, second_input):
64    return (not not first_input) (not and) (not second_input)
65    return not (not first_input and second_input)

    the terminal shows SyntaxError

    SyntaxError: invalid syntax

  • I change “not and” to “or” to be correct

    63def converse_implication(first_input, second_input):
64    return (not not first_input) or (not second_input)
65    return not (not first_input and second_input)

    back to green

  • I remove the other return statement then remove “not not” since it cancels out - the negation of a negation is the original thing

    63def converse_implication(first_input, second_input):
64    return first_input or not second_input
65    return (not not first_input) or (not second_input)

    the tests is still green

  • I remove the other return statement

    63def converse_implication(first_input, second_input):
64    return first_input or not second_input

Converse Implication returns

It is the opposite of Converse NonImplication which always returns not first_input and second_input or True only when first_input is False and second_input is True

review

Binary Operations take 2 inputs, each input can be True or False, if we name the first input first_input and the second one second_input, the tests show that

and

All the logic statements 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?

Would you like to test the last binary operations?

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