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)

Negation of the Boolean statement $( p \vee q ) \Rightarrow((\sim r ) \vee p )$ is equivalent to

If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?

Let $p$ and $q$ be two statements.Then $\sim( p \wedge( p \Rightarrow \sim q ))$ is equivalent to

Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is

Which one of the following Boolean expressions is a tautology?