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