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Question
Examine whether the statement pattern
[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.
Solution
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
| p | q | r | ~q | ~q ∨ r | p → (~q ∨ r) |
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 | T | F | 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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