The negation of the statement "$2 + 3 = 5$ and $8 < 10$" is:

The expression $\sim ( \sim p \to q)$ is logically equivalent to

The statement pattern $(p \land q) \to (r \lor \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

The negation of the contrapositive of the statement $(p \lor \sim q) \to (p \land \sim q)$ is

Consider the following statements:
$r: \text{If } p \to q \text{ is false, then } p \lor q \text{ is false.}$
$s: \text{If } p \leftrightarrow q \text{ is false, then } p \lor q \text{ is false.}$
The truth values of $r \to s$ and $s \to r$ are respectively:

The statement pattern $[(p \vee q) \wedge \sim p] \wedge (\sim q)$ is