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Consider the following statements $P:$ Suman is brilliant; $Q:$ Suman is rich $\boldsymbol{R}$ : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only is Suman is rich" can be expressed as

1) $\sim Q \leftrightarrow \sim P \wedge R$
2) $\sim(P \wedge \sim R) \leftrightarrow Q$
3) $\sim P \wedge(Q \leftrightarrow \sim R)$
4) $\sim(Q \leftrightarrow(P \wedge \sim R))$
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(4)

Explanation

Statement is $(P \wedge \sim R) \leftrightarrow Q$
Negation of the statement is
$$\sim[Q \leftrightarrow(P \wedge \sim R)]$$

by Diamond (75,948 points)

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