Which of the following statement patterns is a contradiction?

The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

Consider the following statements.
$p: \text{If } 3^4 > 4^3, \text{then } 3^3 > 4^1$
$q: \text{The roots of the equation } x^2 - 2x + 2 = 0 \text{ are real if and only if Mumbai is in Maharashtra.}$
$r: \text{Statement } p \text{ is true or statement } q \text{ is false.}$
Which of the following has truth value $T$ (true)?

The minimum number of switches in the simplified form of the following switching circuit is

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

The negation of the statement $\forall x \in N, x^2+x$ is an even number is