Complement of a Set: What do I do when a set contains an element that is not in the Universal Set

Question

Let $U = \{x: x \in \mathbb{N}, x>10 \hspace{4 pt} and \hspace{4 pt} x <40\} , \hspace{4 pt} A = { 5,10,20,40}$

The complement of the set should be

Aᶜ = {All natural numbers between greater than 10 and less than 40 except for 20}

right?

so what do I do with the 5, 10, and 40?

Answer 1

You've correctly concluded$$A^\complement=U\setminus A.$$Note that$$\{5,\,10,\,40\}=A\setminus U.$$If you were to add those elements back in after taking the complement, you'd be left with the symmetric difference$$A\operatorname{\triangle}U=(U\setminus A)\cup(A\setminus U).$$