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Question
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
Sum
Solution
| p | q | ∼p | ∼q | ∼p ∧ ∼q | p → q | (∼p ∧ ∼q) → (p → q) |
| T | T | F | F | F | T | T |
| T | F | F | T | F | F | T |
| F | T | T | F | F | T | T |
| F | F | T | T | T | T | T |
All the entries in the last column of the above truth table are T.
∴ (∼p ∧ ∼q) → (p → q) is a Tautology.
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