Question

If the truth values of statements $p,q,r$ are True, True and False respectively
Statement-1: Statement $\sim \left(p \lor q\right)\land \left(p \lor \sim r\right)\land \left(\sim p \lor \sim q\right)$ is false.
Statement-2 : For given truth values $\sim \left(p \lor q\right)$ is false, $\left(p \lor \sim r\right)$ is true, $\left(\sim p \lor \sim q\right)$ is false.

• A. Statement $-1$ is True, Statement $-2$ is True: Statement $-2$ is NOT a correct explanation for Statement $-1$
• B. Statement $-1$ is True, Statement $-2$ is True: Statement $-2$ is a correct explanation for Statement $-1$
• C. Statement $-1$ is True, Statement $-2$ is False
• D. Statement $-1$ is False, Statement $-2$ is True

Answer 1

Answer: (B)

We have,
$\sim \left(p \lor q\right)\land \left(p \lor \sim r\right)\land \left(\sim p \lor \sim q\right)$
$\Leftrightarrow \left(\sim p \land \sim q\right)\land \left(p \lor \sim r\right)\land \left(\sim p \lor \sim q\right)$
$\Leftrightarrow \left(F \land F\right)\land \left(T \lor T\right)\land \left(F \lor F\right)$
$\Leftrightarrow F\land T\land F$
$\Leftrightarrow F$
Hence, statement $-1$ is True, Statement $-2$ is True: Statement $-2$ is a correct explanation for Statement $-1$ .