Theory question 101
SetsA = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x: 3 < x < 9} are subsets of the universal set U = {2, 3, 4, 5, 6, 7, 8, 9}. Find (a) A ∩ (B ∩ C); (b) (A ∪ B) ∩ (B ∪ C).
Show the model answer
Model answer
C = {4, 5, 6, 7, 8}.
(a) B ∩ C = {7}; A ∩ {7} = ∅ (empty set).
(b) A ∪ B = {2, 3, 4, 6, 7, 8, 9}; B ∪ C = {2, 3, 4, 5, 6, 7, 8, 9}.
(A ∪ B) ∩ (B ∪ C) = {2, 3, 4, 6, 7, 8, 9}.
Explanation
List C first: the integers strictly between 3 and 9.