Let the universal set U be the set of all integers from 1 to 12 inclusive. Define A as the set of even integers in U, and B as the set of integers in U that are multiples of 3. Which of the following sets represents the complement of the union of A and B?

Correct answer

A. {1, 5, 7, 11}

Principle or equation

The complement of a set S with respect to the universal set U is the set of all elements in U that are not in S. The union of sets A and B contains all elements that are in A or in B (or both).

Why this answer is correct

U = {1,2,3,4,5,6,7,8,9,10,11,12}. A = {2,4,6,8,10,12}. B = {3,6,9,12}. A ∪ B = {2,3,4,6,8,9,10,12}. The complement of A ∪ B in U is the set of elements in U not in A ∪ B: {1,5,7,11}.

Example

If U = {1,2,3,4,5}, A = {1,2}, B = {2,3}, then A ∪ B = {1,2,3}, and its complement is {4,5}.