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

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$

Identify the quantifier in the following statement and write the negation of the statement.
There exists a capital for every state in India.

The false statement in the following is

The statement $[(p$ $\rightarrow q) \wedge \sim q]$ $\rightarrow r$ is a tautology,when $r$ is equivalent to

Rewrite the following statement in the form "$p$ if and only if $q$":
$p:$ If you watch television,then your mind is free and if your mind is free,then you watch television.