If the universal set U = {1, 2, 3, ..., 10}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A′ ∩ B)′, where complements are taken with respect to U?
Answer and explanation
Correct answer: {1, 2, 3, 6, 7, 8, 9, 10}
With respect to U, A′ = {4, 5, 6, 7, 8, 9, 10}. Intersecting this set with B = {3, 4, 5} gives A′ ∩ B = {4, 5}. Now take the complement of {4, 5} in U. The remaining elements are {1, 2, 3, 6, 7, 8, 9, 10}. Thus option A is correct; option B is only the intermediate intersection, not its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 6, 7, 8, 9, 10}
Why is this the correct answer?
With respect to U, A′ = {4, 5, 6, 7, 8, 9, 10}. Intersecting this set with B = {3, 4, 5} gives A′ ∩ B = {4, 5}. Now take the complement of {4, 5} in U. The remaining elements are {1, 2, 3, 6, 7, 8, 9, 10}. Thus option A is correct; option B is only the intermediate intersection, not its complement.
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.
