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