Let $p$ and $q$ be two statements. Then $\sim(p \wedge (p \Rightarrow \sim q))$ is equivalent to:

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

Check whether "Or" used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer.
$t:$ You are wet when it rains or you are in a river.

The negation of the Boolean expression $\sim s \vee (\sim r \wedge s)$ is equivalent to

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

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is a...