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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Solution
| p | q | r | ~q | ~q∨r | q→r | p→(q→r) | p→(~q∨r) | ~[p→(q→r)] | [p→(~q∨r)]↔~[p → (q → r)] |
| T | T | T | F | T | T | T | T | F | F |
| T | T | F | F | F | F | F | F | T | F |
| T | F | T | T | T | T | T | T | F | F |
| T | F | F | T | T | T | T | T | F | F |
| F | T | T | F | T | T | T | T | F | F |
| F | T | F | F | F | F | T | T | F | F |
| F | F | T | T | T | T | T | T | F | F |
| F | F | F | T | T | T | T | T | F | F |
All the truth values in the last column are F. Hence, it is contradiction.
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