Question

Assume the following sets:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9]
A = {3, 4, 5, 6}
B = {2, 4, 6, 8}
C = {1, 3, 5, 7}
What are the elements of B ∩ (A ∪ C)? Check all that apply.

a) 4
b) 6
c) 8

Answer 1

The elements of B ∩ (A ∪ C) are 4 and 6.

Step-by-step explanation:

The set A OR C contains all outcomes that lie either in set A or set C. A = {3, 4, 5, 6} and C = {1, 3, 5, 7}, so A OR C = {1, 3, 4, 5, 6, 7}. Then, the intersection of B and the union of A and C, denoted as B ∩ (A ∪ C), is the set of elements that are common to both B and the union of A and C. In this case, B ∩ (A ∪ C) = {4, 6}. Therefore, the correct answers are (a) 4 and (b) 6.