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 statement patterns is a tautology?

The statement $[(p \wedge q)$ $\rightarrow p]$ $\rightarrow (q \wedge \sim q)$ is

The truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of $(\sim p \vee q) \rightarrow (p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow (\sim p \wedge q)$ are respectively:

State whether the "Or" used in the following statement is "exclusive" or "inclusive". Give reasons for your answer.
All integers are positive or negative.

Let $p, q, r$ denote arbitrary statements. Then the logical equivalent of the statement $p \Rightarrow (q \vee r)$ is