The entries in the last column of the truth table for $\sim(p \wedge q)$ are

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

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

The inverse of the proposition $(p \wedge \sim q) \rightarrow r$ is:

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

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :