Problem #WSP-5270

Problem

$A,B$ and $C$ are three sets. Prove that if we take an intersection $A\cap B$ and unite it with the set $C$, we will get the same set as if we took an intersection of two unions $A\cup C$ and $B\cup C$. Essentially, prove that $(A\cap B)\cup C=(A\cup C)\cap (B\cup C)$. Draw a Venn diagram for the set $(A\cap B)\cup C$.