JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Mathematical Reasoning *

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Consider the following statements :
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

(A) $B \to (A \lor C)$
(B) $(\sim B) \land (A \land C)$ ✓ Correct
(C) $B \to ((\sim A) \lor (\sim C))$
(D) $B \to (A \land C)$

Answer: (B)

Solution

The original statement is

(A \land C) \to B

. Its negation is

\sim ((A \land C) \to B) =\sim (\sim (A \land C) \lor B)

. By De Morgan's law, this equals

(A \land C) \land (\sim B)

, which is option (B).

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Mathematical Reasoning *

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