If U = {1,2,3,4,5,6,7,8,9}, A = {1,4,7}, and B = {2,4,8}, what is (A ∪ B)'?
Answer and explanation
Correct answer: {3,5,6,9}
First find the union of A and B by listing every element that appears in either set: A ∪ B = {1,2,4,7,8}. The complement of this union is taken with respect to the universal set U, so remove these elements from U. The remaining elements are U − (A ∪ B) = {3,5,6,9}. Therefore, option A is correct. Option B is the union itself, option C contains only the common element, and option D incorrectly leaves out 9.
Frequently asked questions
What is the correct answer to this question?
{3,5,6,9}
Why is this the correct answer?
First find the union of A and B by listing every element that appears in either set: A ∪ B = {1,2,4,7,8}. The complement of this union is taken with respect to the universal set U, so remove these elements from U. The remaining elements are U − (A ∪ B) = {3,5,6,9}. Therefore, option A is correct. Option B is the union itself, option C contains only the common element, and option D incorrectly leaves out 9.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
