If U = {1,2,3,4,5,6,7,8}, A = {1,2,3,4}, and B = {5,6,7,8}, what is the relation between B and A?
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Answer and explanation
Correct answer: B = Aᶜ
The complement Aᶜ relative to U consists of all elements in U that are not in A. Removing {1,2,3,4} from U = {1,2,3,4,5,6,7,8} leaves {5,6,7,8}, which is exactly B. Hence B = Aᶜ. Also, A and B are disjoint, so their intersection is empty; this shows why option D is false. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
B = Aᶜ
Why is this the correct answer?
The complement Aᶜ relative to U consists of all elements in U that are not in A. Removing {1,2,3,4} from U = {1,2,3,4,5,6,7,8} leaves {5,6,7,8}, which is exactly B. Hence B = Aᶜ. Also, A and B are disjoint, so their intersection is empty; this shows why option D is false. 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.
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