Let U = {1, 2, ..., 12}, A = {2, 3, 5, 7, 11}, and B = {1, 3, 5, 9, 11}. What is (A ∪ B)′, the complement of A ∪ B in U?
Answer and explanation
Correct answer: {4, 6, 8, 10, 12}
The governing concept is that a complement is always taken with respect to the stated universal set. First combine all distinct elements: A ∪ B = {1, 2, 3, 5, 7, 9, 11}. Now remove these elements from U = {1, 2, ..., 12}. The elements left are 4, 6, 8, 10, and 12, so (A ∪ B)′ = {4, 6, 8, 10, 12}. Option B lists the union itself, while option C is only the intersection.
Frequently asked questions
What is the correct answer to this question?
{4, 6, 8, 10, 12}
Why is this the correct answer?
The governing concept is that a complement is always taken with respect to the stated universal set. First combine all distinct elements: A ∪ B = {1, 2, 3, 5, 7, 9, 11}. Now remove these elements from U = {1, 2, ..., 12}. The elements left are 4, 6, 8, 10, and 12, so (A ∪ B)′ = {4, 6, 8, 10, 12}. Option B lists the union itself, while option C is only the intersection.
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.
