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:

