The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge  \sim q} \right)$

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :

Among the statements

$(S1)$: $(p \Rightarrow q) \vee((\sim p) \wedge q)$ is a tautology

$(S2)$: $(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$ is a contradiction

Let $p$ and $q$ be two Statements. Amongst the following, the Statement that is equivalent to $p \to q$ is

The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$

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.