Q: question about universal sets of real numbers If $ A = \{x \in R | x \lt -5 $ or $  x \ge 3\} $ and $ B =\{ x \in R | -7 \lt x \le 3\} $
Find $ (A \cup B)^c$
I figured it to be $\{ x \in R | x \le -7$ $or $ $ x \gt 3 \}$ 
Did I calculate it right? Can you push me in the right direction? 

A: Just to make it graphical. I hope it helps:


A: Note that 
$$A\cup B = \{x \in \mathbb R \mid x \in A \;\text{ or }\;\; x \in B \}$$
$$A\cup B = \{x \in \mathbb R \mid  x \lt -5 \;\;\text{or}\;\;x \geq 3\;\;\text{or}\;\; -7 \lt x \le 3\} = \mathbb R$$
So $$(A \cup B)^c = \mathbb R\setminus(A\cup B) = \mathbb R\setminus \mathbb R = \varnothing$$

A: Well, $x\in A\cup B$ if and only if it is in either one; and it is in the complement if and only if it is not in neither.
What does it mean that $x$ is not in $A$ and not in $B$? It means that $-5\leq x<3$, and either $x<-7$ or $3<x$. Is there such $x$?
