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Question
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Solution
Consider the statement pattern : [(p → q) ∧ q ] → p
No. of rows = 2n = 2 × 2 = 4
No. of column = m + n = 3 + 2 = 5
Thus the truth table of the given logical statement:
[(p → q) ∧ q] → p
| p | q | p → q | (p → q) ∧ q | [(p → q) ∧ q] → p |
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | T | T | F |
| F | F | T | F | T |
The entries in the last column of the above truth table are neither all T nor all F.
∴ [(p → q) ∧ q] → p is contingency.
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