Which of the following is a contradiction?

If $(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p \vee q$ is false,then the truth values of $p, q$ and $r$ are respectively

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)?

Consider the following statement patterns:
$A$. $(q \to p) \vee (p \to q)$
$B$. $(\sim p \vee \sim q) \leftrightarrow \sim (p \wedge q)$
$C$. $[(p \vee q) \wedge \sim p] \wedge \sim q$
$D$. $(p \wedge q) \wedge (\sim p \vee \sim q)$
Which of the following is correct?

What is the dual statement of $p \wedge (\sim p) = c$?

Check whether the following sentence is a statement. Give reasons for your answer.
"How far is Chennai from here?"