The false statement in the following is - Vidyadip

MCQ

The false statement in the following is

A
$\mathrm{p} \wedge(\sim \mathrm{p})$ is a contradiction
B
$\mathrm{p} \vee(\sim \mathrm{p})$ is a tautology
C
$\sim(\sim p) \leftrightarrow p$ is tautology
✓
$(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\sim \mathrm{q} \rightarrow \sim \mathrm{p})$ is a contradiction

✓

Answer

Correct option: D.

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

(D) $p \rightarrow q$ is logically equivalent to $\sim q \rightarrow \sim p$
$\therefore \quad(p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)$ is a tautology
...[Using Shortcut 8]
But, it is given contradiction.
Hence, it is false statement.

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