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Question
The false statement in the following is ______.
Options
p ˄ (∼ p) is contradiction
(p → q) ↔ (∼ q → ∼ p) is a contradiction
∼ (∼ p) ↔ p is a tautology
p ˅ (∼ p) ↔ p is a tautology
Solution
The false statement in the following is (p → q) ↔ (∼ q → ∼ p) is a contradiction.
Explanation:
(p → q) ↔ (∼ q → ∼ p)
| p | q | ∼ p | ∼ q | p → q | ∼ q → ∼ p | (p → q) ↔ (∼ q → ∼ p) |
| T | T | F | F | T | T | T |
| T | F | F | T | F | F | T |
| F | T | T | F | T | T | T |
| F | F | T | T | T | T | T |
In the above table, all the entries in the last column are T. Therefore, the given statement pattern is a tautology.
∴ The false statement is (p → q) ↔ (∼ q → ∼ p) is a contradiction.
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