The negation of the compound statement $\sim p \vee (p \vee (\sim q))$ is

The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

$(p \wedge \sim q) \wedge (\sim p \vee q)$ 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 $\sqrt{2}+\sqrt{3}=\sqrt{5}$.

Which of the following statements is a tautology?

Write the negation of the following statement:
$r:$ For every real number $x$,either $x > 1$ or $x < 1.$