Problem #WSP-5271

Problem

Let $A,B$ and $C$ be three sets. Prove that if we take an intersection $A\cap B$ and intersect it with the set $C$, we will get the same set as if we took an intersection of $A$ with $B\cap C$. Essentially, prove that it does not matter where to put the brackets in $(A\cap B)\cap C=A\cap (B\cap C)$. Draw a Venn diagram for the set $A\cap B\cap C$.
Prove the same for the union $(A\cup B)\cup C=A\cup (B\cup C)=A\cup B\cup C$.