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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: ~(Q↔(P∧~R))

Solution

Let P=intelligent, Q=wealthy, R=truthful so dishonest=~R. The statement 'intelligent and dishonest iff wealthy' is (P AND ~R) <=> Q. Its negation is ~(Q <=> (P AND ~R)), which is option 0.

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