Find the component statements of the following compound statement:
It is raining and it is cold.

Show that the statement "For any real numbers $a$ and $b$,$a^{2}=b^{2}$ implies that $a=b$" is not true by giving a counter-example.

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 pattern $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to

If the truth value of $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then which of the following is $NOT$ true?

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