The negation of the proposition "If $2$ is prime,then $3$ is odd" 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 if and only if Suman is rich" can be equivalently expressed as:

The statement $(p \wedge q) \Rightarrow (p \wedge r)$ is equivalent to:

The negation of the Boolean expression $\sim s \vee (\sim r \wedge s)$ is equivalent to

Let $r \in \{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$ is a tautology. Then $r$ is equal to

Which of the following statements is a tautology?