If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
$\sim (p \wedge q) \Rightarrow (r \wedge s)$
$\sim (p\; \wedge \sim q) \Rightarrow (r \wedge s)$
$\sim (p\; \wedge q)\; \Rightarrow (r \vee s)$
None of these
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to
If $p$ and $q$ are simple propositions, then $p \Rightarrow q$ is false when
The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to
$\sim (p \Leftrightarrow q)$ is