Sum
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
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Solution
| p | q | r | ∼p | ∼q | p ∨ ∼q | ∼p ∧ q | (p ∨ ∼q) ∨ (∼p ∧ q) | (I) ∧ r |
| (I) | ||||||||
| T | T | T | F | F | T | F | T | T |
| T | T | F | F | F | T | F | T | F |
| T | F | T | F | T | T | F | T | T |
| T | F | F | F | T | T | F | T | F |
| F | T | T | T | F | F | T | T | T |
| F | T | F | T | F | F | T | T | F |
| F | F | T | T | T | T | F | T | T |
| F | F | F | T | T | T | F | T | F |
The entries in the last column are neither all T nor all F.
∴ [(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r is a contingency.
Concept: Statement Patterns and Logical Equivalence
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