Write the negation of the following statement:
$s:$ All students study mathematics at the elementary level.

If $p$: It is raining. $q$: Weather is pleasant. Then the simplified form of the statement "It is not true that,if it is raining then the weather is not pleasant" is

What is the identity element for the conjunction $(AND)$ operation in Boolean algebra of logical statements?

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

If the statements $p, q$ and $r$ are true,false and true statements respectively,then the truth value of the statement pattern $[\sim q \wedge (p \vee \sim q) \wedge \sim r] \vee p$ and the truth value of its dual statement respectively are

The entries in the last column of the truth table for $\sim(p \wedge q)$ are