Write the negation of the following statement and check whether the resulting statement is true:
The sum of $3$ and $4$ is $9.$

The converse of "If $3$ is a prime number,then $3$ is odd." is

For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p \wedge q)$ is

Negation of the statement $\forall x \in \mathbb{R}, x^2+1=0$ is

For each of the following compound statements,first identify the connecting words and then break it into component statements.
The sand heats up quickly in the Sun and does not cool down fast at night.

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 $\sqrt{2}+\sqrt{3}=\sqrt{5}$.