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Consider the following statements P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as

1. ~(Q ↔ (P ∧ ~R))
2. ~Q ↔ ~P ∧ R
3. ~(P ∧ ~R) ↔ Q
4. ~P ∧ (Q ↔ ~R)

Correct answer: ~(Q ↔ (P ∧ ~R))

Solution

The correct option negates the biconditional statement by applying De Morgan's laws, which states that the negation of 'A if and only if B' is equivalent to 'not A or not B'. Thus, negating 'Suman is rich if and only if Suman is brilliant and dishonest' correctly leads to the expression in option A.

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