Sum
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ ∼ q) ↔ (p → q)
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Solution
| p | q | ∼ q | p ∧ ∼ q | p → q | (p ∧ ∼ q) ↔ (p → q) |
| T | T | F | F | T | F |
| T | F | T | T | F | F |
| F | T | F | F | T | F |
| F | F | T | F | T | F |
All the entries in the last column of the above truth table are F.
∴ (p ∧ ∼ q) ↔ (p → q) is a contradiction.
[Note: Answer in the textbook is incorrect]
Concept: Statement Patterns and Logical Equivalence
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