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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]
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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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