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

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

Consider the following statements:
$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?

$(p \wedge \sim q) \wedge (\sim p \vee q)$ is

Consider the following statements:
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.

If $p$ and $q$ are true statements and $r$ and $s$ are false statements,then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(p \vee s) \leftrightarrow(q \wedge r)$ are respectively