The statement pattern $p \rightarrow \sim(p \wedge \sim q)$ is equivalent to

The logical expression $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

Which of the following Boolean expressions is not a tautology?

Write the negation of the following statement:
$p:$ For every positive real number $x,$ the number $x-1$ is also positive.

The conditional statement $(p \wedge q) \implies p$ is:

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.