The logical expression $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

Negation of the compound proposition: "If the examination is difficult,then $I$ shall pass if $I$ study hard."

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity,then the triangle is an equilateral triangle" is

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"?

$S_1$: If $-7$ is an integer,then $\sqrt{-7}$ is a complex number.
$S_2$: $-7$ is not an integer or $\sqrt{-7}$ is a complex number.

The negation of the expression $q \vee ((\sim q) \wedge p)$ is equivalent to