Question

2. Let A-(2, 3, 4), B = {3, 4, 5, 6), and suppose the universal set is U-(1,2 all the elements in the following sets. ,9). List (a) (A U B) (b) (ANB) × A (c) P(An B)

Answer 1

Given A = {2, 3, 4} B = {3, 4, 5, 6} U = {1, 2, 3, ....9} n(A) = 3 n(B) = 4 n(U) = 9 (a) (A Union B)' neither A nor B Therefore A Intersection B = {3, 4} (A Union B)' = U -(A Intersection B) (A Union B)' = {1, 2, 5, 6, 7, 8, 9} (b) (A Intersection B) times A A times B = set of all order pair of elements from A & B = {(x, y): x elementof A, y elementof B} (A Intersection B) & A Therefore (A Intersection B) = {(3, 2): (3,3): (3, 4): (4, 2): (4, 3): (4, 4)} \r\n P(A Intersection B) = n(A Intersection B)/n(U) n(A Intersection B) = {3, 4} n(A Intersection B) = 2 Therefore P(A Intersection B) = 2/9