Question

Consider
$\text{Statement-I}:(p\wedge \sim q)\wedge (\sim p\wedge q)$ is fallacy
$\text{Statement-II}:(p\to q)\leftrightarrow (\sim q\to \sim p)$ is tautology

• A. Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I.
• B. Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.
• C. Statement-I is true; Statement-II is false.
• D. Statement-I is false; Statement-II is true.

Answer 1

The correct option is B Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I.

$\text{Statement-II}:(p\to q)\leftrightarrow (\sim q\to \sim p)$
$\Rightarrow (p\to q)\leftrightarrow (p\to q)$
$\therefore$ It is always true
$\text{Statement-I}:(p\wedge \sim q)\wedge (\sim p\wedge q)$
$\Rightarrow p\wedge \sim q\wedge \sim p\wedge q$
$\Rightarrow p\wedge \sim p\wedge \sim q\wedge q$
$\Rightarrow f\wedge f$
$\Rightarrow f$
$\therefore$ It is true
Clearly, Statement-II is not a correct explanation for Statement-I.