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

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which of the following is a tautology?

Consider the following statements:
$P$: $I$ have fever
$Q$: $I$ will take medicine
$R$: $I$ will take rest
The statement "If $I$ have fever,then $I$ will take medicine and $I$ will take rest" is equivalent to:

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 $-x < -y.$

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

For the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?