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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

1. B → (A ∨ C)
2. (~B) ∧ (A ∧ C)
3. B → ((~A) ∨ (~C))
4. B → (A ∧ C)

Correct answer: (~B) ∧ (A ∧ C)

Solution

The correct option represents the negation of a conditional statement by asserting that Rishi is not honest while simultaneously being a judge and not arrogant, which directly contradicts the original implication.

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