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.

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 $-x < -y.$

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively......

If $ab = 0$,write the contrapositive of the statement $(a = 0 \text{ or } b = 0)$.

The negation of $(p \land q) \to ((p \lor r) \to \sim q)$ is equivalent to ...

Consider the following statements:
$P :$ Ramu is intelligent
$Q :$ Ramu is rich
$R :$ Ramu is not honest
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as: