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