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Question
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Solution
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | ~p | ~p ∧ q | p ∨ q | (p∨q) ∧~p |
| T | T | F | F | T | F |
| T | F | F | F | T | F |
| F | T | T | T | T | T |
| F | F | T | F | F | F |
The entries in columns 4 and 6 are identical
∴ ~p ∧ q ≡ (p ∨ q) ∧ ~ p
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