Q53 / 150 · MHT CET 2021 (22 Sep Shift 2) · Mathematics
Given p: A man is a judge, q: A man is honest If $\mathrm{S} 1$ : If a man is a judge, then he is honest S2: If a man is a judge, then he is not honest S3: A man is not a judge or he is honest S4: A man is a judge and he is honest Then
- A$\mathrm{S}_2 \equiv \mathrm{S}_3$
- B$\mathrm{S}_1 \equiv \mathrm{S}_2$
- C$\mathrm{S}_2 \equiv \mathrm{S}_4$
- Correct answerD$\mathrm{S}_1 \equiv \mathrm{S}_3$
Solution
We will write logical form of given statements
$$
\begin{array}{ll}
\mathrm{S}_1=\mathrm{p} \rightarrow \mathrm{q} & \mathrm{S}_2=\mathrm{p} \rightarrow-\mathrm{q} \\
\mathrm{S}_3=\sim \mathrm{p} \vee \mathrm{q} & \mathrm{S}_4=\mathrm{p} \wedge \mathrm{q}
\end{array}
$$
We know that $\mathrm{p} \rightarrow \mathrm{q} \equiv \sim \mathrm{q} \rightarrow \sim \mathrm{p} \equiv \sim(\sim \mathrm{q}) \vee \sim \mathrm{p} \equiv \mathrm{q} \vee \sim \mathrm{p}$
Hence, the correct answer is option: 'D'.