A regular language (also called a rational language) is a formal language that can be expressed using a regular expression.
So, Assume that we have a regular language like $L=L_1 \cup L_2$ and we know that $L_1$ is a finite language. How can we prove that $L_2$ is regular too?
Note: My idea to prove this is that every finite language is a regular language. So, $L_2$ should be regular too. Is this true ? If so, are there better proofs for this?