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:

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

$$\sim P \wedge (Q \leftrightarrow \sim R)$$