2. (20 points) For each pair of sets, determine whether they are disjoint, equal, proper subset or none of the above. Give a justification for each answer. - In order to justify that A and B are equal, you will need to show that any arbitrary element of A is in B and any arbitrary element of B is in A. - In order to justify that A is a proper subset of B, you will need to show that any arbitrary element of A is in B and there exists an element in B that is not in A. - In order to justify that A and B are disjoint then you will need to show that any arbitrary element of A is not in B (or vice versa) - In order to justify none of the above then you will need to show that there exists an element that is in both sets A and B and that there exists an element of A that is not in B and there exists an element in B that is not in A. (a) A={xZx22x} and B={xZx2} (b) A={xRx2Z} and B=Q (c) A={xRx/Q} and B={xRx/Z} (d) A=ZQ and B=QZ (e) A={(x,y)ZZx+y is even } and B={(x,y)ZZx is even and y is even }