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Question
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Solution
~ p ∧ q ≡ (p ∨ q) ∧ ~ p
| 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 |
In the above truth table, the entries in the columns 4 and 6 are identical.
∴ ~p ∧ q ≡ (p ∨ q) ∧ ~p.
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