Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If the sum of digits of a number is divisible by $3,$ then the number is divisible by $3.$
$q:$ If a number is divisible by $3,$ then the sum of its digits is divisible by $3.$

Which of the following sentences are statements? Give reasons for your answer.
The square of a number is an even number.

Write the negation of the following statement:
$q:$ All cats scratch.

The statement $p \rightarrow \sim q$ is false,if

If $(p \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false,then $p$ 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 $\sqrt{2}+\sqrt{3}=\sqrt{5}$.