Write the following statement in the form "if-then":
$A$ quadrilateral is a parallelogram if its diagonals bisect each other.

Negation of $p \wedge (q \wedge \sim(p \wedge q))$ is

$ \sim[(\sim p) \wedge q] $ is logically equivalent to

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
$I$: There exists real numbers $x$ and $y$ for which $x+y=y+x.$
$II$: For all real numbers $x$ and $y$,$x+y \neq y+x.$

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
Two lines intersect at a point or are parallel.

$(S1) (p \Rightarrow q) \vee (p \wedge (\sim q))$ is a tautology. $(S2) ((\sim p) \Rightarrow (\sim q)) \wedge ((\sim p) \vee q)$ is a contradiction. Then