If \(A\cup B=U\) and \(A\cap B=\varnothing\), then which set is equal to \(B\)?
Answer and explanation
Correct answer: \(A'\)
The condition \(A\cup B=U\) says that together the sets cover the entire universal set. The condition \(A\cap B=\varnothing\) says that they have no common elements. Consequently, every element of \(U\) that is not in \(A\) must be in \(B\), and no element of \(A\) can be in \(B\). Therefore, \(B\) is the complement of \(A\) in \(U\), so \(B=A'\).
Frequently asked questions
What is the correct answer to this question?
\(A'\)
Why is this the correct answer?
The condition \(A\cup B=U\) says that together the sets cover the entire universal set. The condition \(A\cap B=\varnothing\) says that they have no common elements. Consequently, every element of \(U\) that is not in \(A\) must be in \(B\), and no element of \(A\) can be in \(B\). Therefore, \(B\) is the complement of \(A\) in \(U\), so \(B=A'\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
