If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7}, what is A ∩ Bᶜ?
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Answer and explanation
Correct answer: {1,2,3}
The complement Bᶜ is taken with respect to U, so Bᶜ = U − B = {1,2,3,8,9,10}. Now intersect this set with A = {1,2,3,4,5}. The common elements are only 1, 2, and 3. Therefore, A ∩ Bᶜ = {1,2,3}, which is option A. The elements 4 and 5 are excluded because they belong to B.
Frequently asked questions
What is the correct answer to this question?
{1,2,3}
Why is this the correct answer?
The complement Bᶜ is taken with respect to U, so Bᶜ = U − B = {1,2,3,8,9,10}. Now intersect this set with A = {1,2,3,4,5}. The common elements are only 1, 2, and 3. Therefore, A ∩ Bᶜ = {1,2,3}, which is option A. The elements 4 and 5 are excluded because they belong to B.
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.
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