Which of the following statement patterns is a tautology?

The expression $\sim (p \vee q) \vee (\sim p \wedge q)$ is equivalent to:

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

The negation of the statement "If $I$ become a teacher,then $I$ will open a school" is

The given circuit is equivalent to:

For each of the following compound statements,first identify the connecting words and then break it into component statements.
The sand heats up quickly in the Sun and does not cool down fast at night.