The Boolean expression $\sim (p \Rightarrow (\sim q))$ is equivalent to

The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

If $c$ denotes the contradiction,then the dual of the compound statement $\sim p \wedge (q \vee c)$ is:

What is the dual statement of the statement "Rina is healthy and Mina is beautiful"?

Which of the following statements is correct?
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency