1. Sets notation Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: AnB 0, AnC=0 BEC, AED ACD, BD ACN, BCN i. Write the sets out explicitly in terms of the elements, i.e., do not write "A", "B" as members of any of the sets. ii. After writing the sets out, show that each of the conditions are satisfied with brief explana- tions where appropriate. 2. The power set i. Let A {1,2,3} and let p be a relation on P(A) x Z that maps a set to its cardinality, e.g. ({1,2}, 2) E p. (The notation P(A) denotes the powerset of A) What is the set BC Z with the fewest elements such that p C P(A) x B? Provide a written justification as well as the set B itself. ii. For two non-empty sets E, F, explain whether or not it is possible that both E E F and ECF. iii. For two non-empty sets E, F, explain whether or not it is possible that both EE P(F) and ECP(F)