The statement $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

$(p \wedge \sim q \wedge \sim r) \vee (\sim p \wedge q \wedge \sim r) \vee (\sim p \wedge \sim q \wedge r)$ is equivalent to-

Let $\Delta, \nabla \in \{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta ( p \nabla q )$ is a tautology. Then

The negation of $(p \land q) \to ((p \lor r) \to \sim q)$ is equivalent to

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)?

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If $a$ and $b$ are integers,then $ab$ is a rational number.