If $p$ and $q$ are true statements and $r$ and $s$ are false statements,then the truth values of the statement patterns $(p \wedge q) \vee r$ and $(p \vee s) \leftrightarrow(q \wedge r)$ are respectively

The contrapositive of $(\sim p \wedge q) \rightarrow (q \wedge \sim r)$ is

Given $p$: $A$ man is a judge,$q$: $A$ man is honest. If $S_1$: If a man is a judge,then he is honest; $S_2$: If a man is a judge,then he is not honest; $S_3$: $A$ man is not a judge or he is honest; $S_4$: $A$ man is a judge and he is honest. Then:

$\sim (p \Leftrightarrow q) = \dots$

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

The statement $p \to (q \to p)$ is equivalent to