5.6.34. (a) Find an example of set A and a nonempty subset B C A, such that A and A \ B have the same cardinality.

Prove the following...

(10) Write each of the following sets in the form of listing its elements (i.e. in the form {a,b,c} to denote the set containing the three elements a, b and c.) ) What is P({0})? P(A), where A:= {b, A, &}. }

1. Let A = {-30, -10, 10, 30, 50} and B = {-20, -10, 0, 10} be subsets of the universal set ε = {10x x € ZZ and -3≤ x <6}. (a) List the elements of An B and (AUB)'. (b) Evaluate: (i) │A\ B|; (ii) |A × B|; [1] (iii) |P(A)|; (iv) P(B) × P(A)|. [2] (c) Are the following statements are true or false? Explain your reasoning. (i) 0 СА; (ii) {0} = P(A); (iii) {10} E AUB; (iv) {10} is a proper subset of An B. (d) List the elements of P(A) P(B). [2] [2] (e) If the set C is also a subset of Ɛ, with |C| = 5, An C = {-10, 30} and BNC {-10, 20}, list the elements of C. = [2]