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Question
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
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Solution
| p | q | ¬p | p v q | ¬(p v q) | ¬p ∧ q | ¬(p v q) v (¬p ∧ q) |
| T | T | F | T | F | F | F |
| T | F | F | T | F | F | F |
| F | T | T | T | F | T | T |
| F | F | T | F | T | F | T |
From the table, it is clear that ¬P
¬(p v q) v (¬p ∧ q) are logically equivalent
i.e. ¬(p v q) v (¬p ∧ q) ≡ ¬p
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