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

Consider the following statements:
$P$: Suman is brilliant
$Q$: Suman is rich
$R$: Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as:

The contrapositive of the statement "$I$ go to school if it does not rain" is

For each of the following compound statements,first identify the connecting words and then break it into component statements.
$x=2$ and $x=3$ are the roots of the equation $3x^{2} - x - 10 = 0$.

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

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
Students can take French or Sanskrit as their third language.