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

State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
All integers are positive or negative.

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be:

The contrapositive of $\sim q \to p$ is equivalent to

The simplified switching circuit for the following circuit is

The contrapositive of $\sim q \to p$ is equivalent to