Which of the following is a contradiction?

If $p$: switch $S_1$ is closed,$q$: switch $S_2$ is closed,$r$: switch $S_3$ is closed,then the symbolic form of the following switching circuit is equivalent to:

The maximum number of compound propositions,out of $p \vee r \vee s$,$p \vee \sim r \vee \sim s$,$p \vee \sim q \vee s$,$\sim p \vee \sim r \vee s$,$\sim p \vee \sim r \vee \sim s$,$\sim p \vee q \vee \sim s$,$q \vee r \vee \sim s$,$q \vee \sim r \vee \sim s$,$\sim p \vee \sim q \vee \sim s$ that can be made simultaneously true by an assignment of the truth values to $p, q, r$ and $s$,is equal to

The statement $(p \wedge (\sim q))$ $\Rightarrow (p$ $\Rightarrow (\sim q))$ is

The expression $\sim ( \sim p \to q)$ is logically equivalent to

Using the words "necessary and sufficient",rewrite the statement "The integer $n$ is odd if and only if $n^{2}$ is odd". Also,check whether the statement is true.