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Given the statements P : Suman is intelligent Q : Suman is wealthy R : Suman is truthful Which of the following represents the negation of the statement “Suman is intelligent and dishonest if and only if Suman is wealthy” ?

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

Correct answer: (~P∧~R)↔Q

Solution

The correct option represents the negation of the original statement by flipping the conditions of the biconditional relationship, which indicates that if Suman is neither intelligent nor truthful, then Suman is wealthy. This captures the essence of negating the original 'if and only if' statement.

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