The proposition $p \Rightarrow \sim (p \wedge \sim q)$ is

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

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

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

Let $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.

The negation of the statement "$12$ is a multiple of $3$ and $12$ is a multiple of $4$" is: