Which of the following is true?

If truth values of statements $p, q$ are true,and $r, s$ are false,then the truth values of the following statement patterns are respectively:
$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$
$b: (\sim q \wedge \sim r) \leftrightarrow(p \vee s)$
$c: (\sim p \vee q) \rightarrow(r \wedge \sim s)$

The statement $(P$ $\Rightarrow Q) \wedge (R$ $\Rightarrow Q)$ is logically equivalent to:

The negation of the statement "For all real numbers $x$ and $y, x+y=y+x$" is

Check whether the following sentence is a statement. Give reasons for your answer.
"The sun is a star."

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?