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

Which of the following statements has the truth value $T$?
$A$: Cube roots of unity are in Geometric Progression and their sum is $0$.
$B$: $4+7 > 10$ iff $2+8 < 10$.
$C$: $\exists x \in N$ such that $x^2-3x+2=0$ and $\exists n \in N$ such that $n$ is an odd number.
$D$: $3+i$ is a complex number or $\sqrt{2}+\sqrt{3}=\sqrt{5}$.

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...

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

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

The statement $(p$ $\rightarrow q)$ $\rightarrow ((\sim p$ $\rightarrow q)$ $\rightarrow q)$ is