Regular Language – Properties of the Union and Intersection of Regular and Non-Regular Languages

Question

Given $L_1$ is a regular language and $L_2$ is a non-regular language.
$\Longrightarrow$ then $L_1\cap L_2$ (the intersection) is non-regular OR $L_1\cup L_2$ (the union) is non-regular.

Is it true or false?
Can you give an example/proof?

Answer 1

Hint. Observe that $L_2 = (L_1 \cup L_2) \cap \bigl(L_1^c \cup (L_1 \cap L_2)\bigr)$.