question_answer

Consider the following statements

P: Suman is brilliant

Q: Suman is rich

R: Suman is honest.

The negative of the statement. "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

A)  \[\sim (Q\leftrightarrow (P\wedge \sim R))\]

B)  \[\sim Q\leftrightarrow \,\sim P\wedge R\]

C)  \[\sim (P\wedge \sim R)\leftrightarrow Q\]  

D)  \[\sim P\wedge (Q\leftrightarrow \,\sim R)\]

E)  None of these