Negating an Existential Quantification

The statement

‘ There is a student in your class who has taken a course in calculus ’

\exists x Q (x)

where $Q (x)$ is the statement $‘ x has taken a course in calculus ’$ and the domain consists of all the students in you class
What is the negation?

\begin{aligned} ‘ & It is not the case that \\ there exists a student in your class who has taken a course in calculus ’ \end{aligned}

How can this also be expressed?

‘ Every student in you class has not taken a course in calculus ’

Therefore...

\neg \exists x Q (x) \equiv \forall x \neg Q (x)