The negation of the statement
"If I become a teacher, then I will open a school", is
I will become a teacher and I will not open a school.
Either I will not become a teacher or I will not open a school.
Neither I will become a teacher nor I will open a school
I will not become a teacher or I will open a school.
The statement $\sim[p \vee(\sim(p \wedge q))]$ is equivalent to
The proposition $p \Rightarrow \;\sim (p\; \wedge \sim \,q)$ is
$(p\rightarrow q) \leftrightarrow (q \vee ~ p)$ is
$\sim ((\sim p)\; \wedge q)$ is equal to
$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.