The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to

Which of the following is a contradiction

If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is

Which of the following is a tautology?

The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to

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 equivalently expressed as