Write the negation of the following statement:
Every natural number is an integer.

Let $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.

Negation of the statement $(p \vee r) \Rightarrow (q \vee r)$ 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 negation of $(p$ $\Rightarrow q)$ $\Rightarrow (q$ $\Rightarrow p)$ is

If the statement $p \vee \sim(q \wedge r)$ is false,then the truth values of $p, q$ and $r$ are respectively: