If $p, q$ are true and $r$ is a false statement, then which of the following is a true statement?

The dual of the statement $~(p\vee q)\wedge \left[p\vee ~(q\wedge ~r)\right]$ is

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 iff Suman is rich" can be expressed as

Simplified form of the switching circuit given below is