Negating a statement with a interval

Question

Hi could anyone help me i am trying to negate a statement that has a interval [0,3], would it become the intervals: [-infinity,0] and [4,+infinity]

Answer 1

If $x\in\mathbb R$ but $x\not\in[0,3]$, then $x\in(-\infty,0)\cup(3,\infty)$.

(To indicate that one of the endpoints is to be excluded from the set,

the corresponding square bracket can be replaced with a parenthesis.)