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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]
Solution
| p | q | ~p | ~q | p∧q | (p∧q)∨(~p) | p∧~q | [(p∧q)∨(~p)]∨[p∧(~q)] |
| T | T | F | F | T | T | F | T |
| T | F | F | T | F | F | T | T |
| F | T | T | F | F | T | F | T |
| F | F | T | T | F | T | F | T |
All the truth values in the last column are T. Hence, it is a tautology.
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