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Question
Show that ¬(p → q) ≡ p ∧¬q
Solution
| p | q | p → q | ¬(p → q) | ¬q | p ∧¬q |
| T | T | T | F | F | F |
| T | F | F | T | T | T |
| F | T | T | F | F | F |
| F | F | T | F | T | F |
The entries in the columns corresponding to ¬(p → q) and p ∧ ¬q are identical and hence they are equivalent.
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