The proposition $(p$ $\Rightarrow \sim p) \wedge (\sim p$ $\Rightarrow p)$ is a

The negation of the statement $\forall x \in N, x^2+x$ is an even number is

Which of the following statements is a tautology?

Write the contrapositive of the following statement:
If a number is divisible by $9,$ then it is divisible by $3.$

Which of the following statement patterns is a contradiction?

Let $a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$ and $b: (p \vee s) \leftrightarrow(q \wedge r)$. If the truth values of $p$ and $q$ are $T$ and that of $r$ and $s$ are $F$,then the truth values of $a$ and $b$ are respectively...