If $p:$ Seema is fat. $q:$ She is happy,then the logical equivalent statement of 'If Seema is fat,then she is happy' is

If $P$ and $Q$ are two statements,then which of the following compound statements is a tautology?

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

$ \sim[(\sim p) \wedge q] $ is logically equivalent to

For the statements $p$ and $q$,consider the following compound statements :
$(a)$ $(\sim q \wedge (p$ $\rightarrow q))$ $\rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?

If $p$: It rains today,$q$: $I$ go to school,$r$: $I$ shall meet my friend,and $s$: $I$ shall go for a movie,then which of the following represents 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"?