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Question
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Solution
| p | q | p ↔ q | ¬(p ↔ q) | ¬q | p ↔ ¬q |
| T | T | T | T | F | F |
| T | F | F | F | T | T |
| F | T | T | F | T | T |
| F | F | F | T | F | F |
From the table, it is clear that
¬(p ↔ q) ≡ p ↔ ¬q
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