MHT CET · Maths · Mathematical Reasoning

Let p : A man is judge.
\(\mathrm{q}: \mathrm{He}\) is honest.
The inverse of \(p \rightarrow q\) is

A If a man is judge, then he is honest.
B If a man is not judge, then he is not honest.
C If a man is honest, then he is judge.
D If a man is not honest then, he is not judge.

Verified Solution

Answer & Solution

Correct Answer

(B) If a man is not judge, then he is not honest.

Step-by-step Solution

Detailed explanation

Inverse of \(p \rightarrow q\) is \(\sim p \rightarrow \sim q\) i.e., If a man is not judge, then he is not honest.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let p : A man is judge.\(\mathrm{q}: \mathrm{He}\) is honest.The inverse of \(p \rightarrow q\) is

Step-by-step Solution

Let p : A man is judge.
\(\mathrm{q}: \mathrm{He}\) is honest.
The inverse of \(p \rightarrow q\) is