The logical statement $\sim(p \vee q) \vee(\sim p \wedge q)$ is equivalent to

The symbolic form of the statement "If it does not rain today or $I$ will not go to school,then $I$ will meet my friend and $I$ will go to watch a movie" is:
$p$: It rains today
$q$: $I$ am going to school
$r$: $I$ will meet my friend
$s$: $I$ will go to watch a movie

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:
$p$ : There is a rational number $x \in S$ such that $x > 0$.
Which of the following statements is the negation of the statement $p$?

The number of choices of $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$,such that $(p \Delta q) \Rightarrow ((p \Delta \sim q) \vee ((\sim p) \Delta q))$ is a tautology,is

Negation of the statement $\forall x \in \mathbb{R}, x^2+1=0$ is

The false statement in the following is