Question

If U = {1, 2, 3, .. ,15}, A = {2, 4}, B = {3, 4, 6, 10, 12, 15}, then (A U C)^c is:

• A. {1,2, 3, 5,15}
• B. {1,3, 5, 6,7, 8, 9, 10,11, 12, 13,14, 15}
• C. {1, 5, 7, 8, 9, 11, 13, 14}
• D. {3, 4, 6, 10, 12,15}

Answer 1

The correct option is C

{1, 5, 7, 8, 9, 11, 13, 14}

The complement of the union of two sets is the intersection of their complements.

A U B = {2, 3, 4, 6, 10, 12, 15}

(A U B)^c = {1, 5, 7, 8, 9, 11, 13, 14}