truth table: Binary Operations


The last chapter covered 2 types of operations. Nullary Operations which do not take input, and Unary Operations which take 1 input.

There are also Binary Operations, these take 2 inputs. Each of the inputs in this exercise will be True or False which means there are 4 possible ways the inputs can be sent to an operation

first input

second input

True

True

True

False

False

True

False

False

These combinations give 16 binary operations, each operations returns True or False when it gets input. Here are the 16 operations that are covered in these chapters and what they return

operation

return

contradiction

False

converse_implication

first or not second

converse_non_implication

not first and second

exclusive_disjunction

(not (first and second)) and (first or second)

logical_conjunction

first and second

logical_disjunction

first or second

logical_equality

(not first or second) and (first or not second)

logical_nand

not (first and second)

logical_nor

not (first or second)

material_implication

not first or second

material_non_implication

first and not second

negate_first

not first

negate_second

not second

project_first

first

project_second

second

tautology

True


preview

Here are the tests I have at the end of the chapters

  1import src.truth_table
  2import unittest
  3
  4
  5class TestBinaryOperations(unittest.TestCase):
  6
  7    def test_contradiction(self):
  8        self.assertFalse(
  9            src.truth_table.contradiction(True, True)
 10        )
 11        self.assertFalse(
 12            src.truth_table.contradiction(True, False)
 13        )
 14        self.assertFalse(
 15            src.truth_table.contradiction(False, True)
 16        )
 17        self.assertFalse(
 18            src.truth_table.contradiction(False, False)
 19        )
 20
 21    def test_logical_conjunction(self):
 22        self.assertTrue(
 23            src.truth_table.logical_conjunction(True, True)
 24        )
 25        self.assertFalse(
 26            src.truth_table.logical_conjunction(True, False)
 27        )
 28        self.assertFalse(
 29            src.truth_table.logical_conjunction(False, True)
 30        )
 31        self.assertFalse(
 32            src.truth_table.logical_conjunction(False, False)
 33        )
 34
 35    def test_project_second(self):
 36        self.assertTrue(
 37            src.truth_table.project_second(True, True)
 38        )
 39        self.assertFalse(
 40            src.truth_table.project_second(True, False)
 41        )
 42        self.assertTrue(
 43            src.truth_table.project_second(False, True)
 44        )
 45        self.assertFalse(
 46            src.truth_table.project_second(False, False)
 47        )
 48
 49    def test_converse_non_implication(self):
 50        self.assertFalse(
 51            src.truth_table.converse_non_implication(True, True)
 52        )
 53        self.assertFalse(
 54            src.truth_table.converse_non_implication(True, False)
 55        )
 56        self.assertTrue(
 57            src.truth_table.converse_non_implication(False, True)
 58        )
 59        self.assertFalse(
 60            src.truth_table.converse_non_implication(False, False)
 61        )
 62
 63    def test_negate_first(self):
 64        self.assertFalse(src.truth_table.negate_first(True, True))
 65        self.assertFalse(src.truth_table.negate_first(True, False))
 66        self.assertTrue(src.truth_table.negate_first(False, True))
 67        self.assertTrue(src.truth_table.negate_first(False, False))
 68
 69    def test_logical_nand(self):
 70        self.assertFalse(src.truth_table.logical_nand(True, True))
 71        self.assertTrue(src.truth_table.logical_nand(True, False))
 72        self.assertTrue(src.truth_table.logical_nand(False, True))
 73        self.assertTrue(src.truth_table.logical_nand(False, False))
 74
 75    def test_tautology(self):
 76        self.assertTrue(src.truth_table.tautology(True, True))
 77        self.assertTrue(src.truth_table.tautology(True, False))
 78        self.assertTrue(src.truth_table.tautology(False, True))
 79        self.assertTrue(src.truth_table.tautology(False, False))
 80
 81    def test_logical_disjunction(self):
 82        self.assertTrue(
 83            src.truth_table.logical_disjunction(True, True)
 84        )
 85        self.assertTrue(
 86            src.truth_table.logical_disjunction(True, False)
 87        )
 88        self.assertTrue(
 89            src.truth_table.logical_disjunction(False, True)
 90        )
 91        self.assertFalse(
 92            src.truth_table.logical_disjunction(False, False)
 93        )
 94
 95    def test_exclusive_disjunction(self):
 96        self.assertFalse(src.truth_table.exclusive_disjunction(True, True))
 97        self.assertTrue(src.truth_table.exclusive_disjunction(True, False))
 98        self.assertTrue(src.truth_table.exclusive_disjunction(False, True))
 99        self.assertFalse(src.truth_table.exclusive_disjunction(False, False))
100
101    def test_material_non_implication(self):
102        self.assertFalse(
103            src.truth_table.material_non_implication(True, True)
104        )
105        self.assertTrue(
106            src.truth_table.material_non_implication(True, False)
107        )
108        self.assertFalse(
109            src.truth_table.material_non_implication(False, True)
110        )
111        self.assertFalse(
112            src.truth_table.material_non_implication(False, False)
113        )
114
115    def test_project_first(self):
116        self.assertTrue(src.truth_table.project_first(True, True))
117        self.assertTrue(src.truth_table.project_first(True, False))
118        self.assertFalse(src.truth_table.project_first(False, True))
119        self.assertFalse(src.truth_table.project_first(False, False))
120
121    def test_converse_implication(self):
122        self.assertTrue(src.truth_table.converse_implication(True, True))
123        self.assertTrue(src.truth_table.converse_implication(True, False))
124        self.assertFalse(src.truth_table.converse_implication(False, True))
125        self.assertTrue(src.truth_table.converse_implication(False, False))
126
127    def test_negate_second(self):
128        self.assertFalse(src.truth_table.negate_second(True, True))
129        self.assertTrue(src.truth_table.negate_second(True, False))
130        self.assertFalse(src.truth_table.negate_second(False, True))
131        self.assertTrue(src.truth_table.negate_second(False, False))
132
133    def test_logical_nor(self):
134        self.assertFalse(src.truth_table.logical_nor(True, True))
135        self.assertFalse(src.truth_table.logical_nor(True, False))
136        self.assertFalse(src.truth_table.logical_nor(False, True))
137        self.assertTrue(src.truth_table.logical_nor(False, False))
138
139    def test_logical_equality(self):
140        self.assertTrue(src.truth_table.logical_equality(True, True))
141        self.assertFalse(src.truth_table.logical_equality(True, False))
142        self.assertFalse(src.truth_table.logical_equality(False, True))
143        self.assertTrue(src.truth_table.logical_equality(False, False))
144
145    def test_material_implication(self):
146        self.assertTrue(src.truth_table.material_implication(True, True))
147        self.assertFalse(src.truth_table.material_implication(True, False))
148        self.assertTrue(src.truth_table.material_implication(False, True))
149        self.assertTrue(src.truth_table.material_implication(False, False))
150
151
152# Exceptions seen
153# AttributeError
154# TypeError
155# AssertionError
156# SyntaxError

requirements

truth table: Nullary and Unary Operations


Binary Operations


what is next?

are you ready to test Binary Operations?