QUESTION
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
SOLUTION
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | ~p | ~p∨q | p∧(~p∨q) | p∧q |
| T | T | F | T | T | T |
| T | F | F | F | F | F |
| F | T | T | T | F | F |
| F | F | T | T | F | F |
In the above truth table, the entries in columns 5 and 6 are identical.
∴ p ∧ (~p ∨ q) ≡ p ∧ q
