Let $p$ and $q$ be any two logical statements and $r: p \to (\sim p \vee q)$. If $r$ has a truth value $F$,then the truth values of $p$ and $q$ are respectively

If statements $p$ and $q$ are true and $r$ and $s$ are false,then the truth values of $\sim(p \rightarrow q) \leftrightarrow (p \wedge s)$ and $(\sim p \rightarrow q) \wedge (r \leftrightarrow s)$ are respectively:

$\sim p \wedge q$ is logically equivalent to

If $\sim p \lor q$ is false, then which of the following is correct?

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:
$p$ : There is a rational number $x \in S$ such that $x > 0$.
Which of the following statements is the negation of the statement $p$?

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow [\sim r \wedge q]$ is False,then which of the following has truth value False?