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Question
Prove that the following statement pattern is a contradiction.
(p → q) ∧ (p ∧ ~ q)
Solution
| p | q | ~q | p→q | p∧~q | (p→q)∧(p∧~q) |
| T | T | F | T | F | F |
| T | F | T | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | F | F |
All the truth values in the last column are F. Hence, it is a contradiction.
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