The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
$P \vee Q$
$\sim(P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$
$P \wedge \sim Q$
$\sim(P \Rightarrow Q)$
If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?
$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is
Negation is $“2 + 3 = 5$ and $8 < 10”$ is
The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to