Dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is

Consider the following three statements :

$(A)$ If $3+3=7$ then $4+3=8$.

$(B)$ If $5+3=8$ then earth is flat.

$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$. Then, which of the following statements is correct?

The number of values of $r \in\{p, q, \sim p , \sim q \}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is:

Which Venn diagram represent the truth of the statement“Some teenagers are not dreamers”

The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to

The negation of the statement $(p \vee q)^{\wedge}(q \vee(\sim r))$ is