Question

If the truth values of statements $p,q,r$ are True, True and False respectively
Statement-1: Statement $∼\left(p∨q\right)âˆ\S \left(p∨∼r\right)âˆ\S \left(∼p∨∼q\right)$ is false.
Statement-2 : For given truth values $∼\left(p∨q\right)$ is false, $\left(p∨∼r\right)$ is true, $\left(∼p∨∼q\right)$ 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,
$∼\left(p∨q\right)âˆ\S \left(p∨∼r\right)âˆ\S \left(∼p∨∼q\right)$
$⇔\left(∼pâˆ\S ∼q\right)âˆ\S \left(p∨∼r\right)âˆ\S \left(∼p∨∼q\right)$
$⇔\left(Fâˆ\S F\right)âˆ\S \left(T∨T\right)âˆ\S \left(F∨F\right)$
$⇔Fâˆ\S Tâˆ\S F$
$⇔F$
Hence, statement $−1$ is True, Statement $−2$ is True: Statement $−2$ is a correct explanation for Statement $−1$ .