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

  $\; \sim \left( {{\rm{Q}} \leftrightarrow \left( {{\rm{P}} \wedge {\rm{\;}} \sim {\rm{R}}} \right)} \right)$

• B

  $ \sim {\rm{Q}} \leftrightarrow {\rm{\;}} \sim {\rm{P}} \wedge {\rm{R}}$

• C

  ${\rm{\;}} \sim \left( {{\rm{P}} \wedge {\rm{\;}} \sim {\rm{R}}} \right) \leftrightarrow Q$

• D

  $\; \sim P \wedge \left( {{\rm{Q\;}} \leftrightarrow \sim {\rm{R}}} \right)$