1 Construct a counter-example for the following statement: for any sets A,B,C, A intersect (B union C) = (A intersect B) union C. 2 Draw diagrams that illustrate the truth of the statement that for all sets A,B,C A intersect (B union C) = (A intersect B) union (A intersect C). 3. Let D_n denote the set of natural numbers that divide n exactly. Write down the sets D_84 and D_60 intersect D_84. Find a number m such that D_m = D_60 intersect D_84. Is it true that for any natural numbers r and s there is a natural number m such that D_m = D_r intersect D_s?