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

If the Boolean expression $(p \wedge q) \circledast (p \otimes q)$ is a tautology,then $\circledast$ and $\otimes$ are respectively given by

Among the two statements:
$(S1): (p \Rightarrow q) \wedge (q \wedge (\sim q))$ is a contradiction and
$(S2): (p \wedge q) \vee ((\sim p) \wedge q) \vee (p \wedge (\sim q)) \vee ((\sim p) \wedge (\sim q))$ is a tautology.

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 $-x < -y.$

Which of the following statements is true?

Which of the following are pairs of equivalent circuits?