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 \((A\cup B)\cup C = A\cup (B\cup C) = A\cup B\cup C\).