If U = {1, 2, ..., 8}, A = {1, 2, 5}, and B = {2, 4, 6}, what is A' ∪ B', where the complement is taken with respect to U?
Answer and explanation
Correct answer: {1, 3, 4, 5, 6, 7, 8}
Using De Morgan’s law, A' ∪ B' = (A ∩ B)'. The common elements of A = {1, 2, 5} and B = {2, 4, 6} are A ∩ B = {2}. Taking the complement of {2} in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8} removes 2 and retains every other element, giving {1, 3, 4, 5, 6, 7, 8}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 4, 5, 6, 7, 8}
Why is this the correct answer?
Using De Morgan’s law, A' ∪ B' = (A ∩ B)'. The common elements of A = {1, 2, 5} and B = {2, 4, 6} are A ∩ B = {2}. Taking the complement of {2} in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8} removes 2 and retains every other element, giving {1, 3, 4, 5, 6, 7, 8}. Therefore, option A is correct.
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.
