The false statement in the following is _____. - Vidyadip

MCQ

The false statement in the following is _____.

A
$p \wedge(\sim p)$ is contradiction
✓
$(p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)$ is a contradiction
C
$\sim(\sim p) \leftrightarrow p$ is a tautology
D
$p \vee(\sim p) \leftrightarrow p$ is a tautology

✓

Answer

Correct option: B.

$(p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)$ is a contradiction

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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