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Question
Prove that q → p ≡ ¬p → ¬q
Solution
| p | q | q → p | ¬p | ¬q | ¬p → ¬q |
| T | T | T | F | F | T |
| T | F | T | F | T | T |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
The entries in the columns corresponding to q → p and ¬p → ¬q are identical and hence they are equivalent.
∴ q → q = ¬p → ¬q
Hence proved.
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