Sum
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(∼ p → q) ∧ (p ∧ r)
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Solution
| p | q | r | ∼ p | ∼ p → q | p ∧ r | (∼ p → q) ∧ (p ∧ r) |
| T | T | T | F | T | T | T |
| T | T | F | F | T | F | F |
| T | F | T | F | T | T | T |
| T | F | F | F | T | F | F |
| F | T | T | T | T | F | F |
| F | T | F | T | T | F | F |
| F | F | T | T | F | F | F |
| F | F | F | T | F | F | F |
The entries in the last column of the above truth table are neither all T nor all F.
∴ (∼ p → q) ∧ (p ∧ r) is a contingency.
Concept: Statement Patterns and Logical Equivalence
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