Question

Let U = (1, 2, 3, 4, 5) be a universal set with subsets A = (2, 4} and B = (1, 5).

List the elements in each of the following sets.
(a) A'
(b) A' n B'
(c) AUB
(d) (AU BY)
If A = (r,s, t] and B = (s, t, u): list the elements in B x A.

Answer 1

(a) A' is the complement of set A, which consists of all the elements in the universal set U that are not in set A. In this case, A' = {1, 3, 5}.

(b) A' n B' is the intersection of the complements of sets A and B. It consists of the elements that are not in set A and not in set B. In this case, A' n B' = {3}.

(c) AUB is the union of sets A and B, which consists of all the elements that are in either set A or set B. In this case, AUB = {1, 2, 4, 5}.

(d) (AU B) represents the symmetric difference of sets A and B, which consists of all the elements that are in either set A or set B, but not in both. In this case, (AU B) = {1, 2, 4, 5}.

If A = (r, s, t] and B = (s, t, u), then B x A represents the cartesian product of sets B and A, which consists of all possible ordered pairs where the first element is from set B and the second element is from set A. In this case, B x A = {(s, r), (s, s), (s, t), (t, r), (t, s), (t, t), (u, r), (u, s), (u, t)}.