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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
Solution
| p | q | r | ~p | ~q | ~p∧q | q∧r | (~p∧q)∧(q∧r) | [(~p∧q)∧(q∧r)]∨(~q) |
| T | T | T | F | F | F | T | F | F |
| T | T | F | F | F | F | F | F | F |
| T | F | T | F | T | F | F | F | T |
| T | F | F | F | T | F | F | F | T |
| F | T | T | T | F | T | T | T | T |
| F | T | F | T | F | T | F | F | F |
| F | F | T | T | T | F | F | F | T |
| F | F | F | T | T | F | F | F | T |
Truth values in the last column are not identical. Hence, it is contingency.
Notes
The answer in the textbook is incorrect.
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