The negative of the statement $\sim p \wedge(p \vee q)$ is

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

If $p, q, r$ are simple propositions, then $(p \wedge q) \wedge (q \wedge r)$ is true then

The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to

Which of the following statement is a tautology?

Which of the following Venn diagram corresponds to the statement “All mothers are women” ($M$ is the set of all mothers, $W$ is the set of all women)