If $\sim p \to q$ is false and $q \leftrightarrow r$ is false, then the truth value of $(p, q, r)$ is...

$(\sim (\sim p)) \wedge q$ is equal to .........

Consider the following statements.
$p$: If $3^4 > 4^3$, then $3^3 > 4^4$
$q$: The roots of the equation $x^2 - 2x + 2 = 0$ are real if and only if Mumbai is in Maharashtra.
$r$: Statement $p$ is true or statement $q$ is false.
Which of the following has truth value $T$ (true)?

Which of the following statement patterns is a contradiction?
$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$
$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_{3} \equiv (p \vee q) \rightarrow \sim p$
$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$

Which of the following statements is logically equivalent to $\sim (p \leftrightarrow q)$?

For integers $m$ and $n$,both greater than $1$,consider the following three statements:
$P$: $m$ divides $n$
$Q$: $m$ divides $n^2$
$R$: $m$ is prime
Which of the following statements is true?