If, with respect to the universal set, \(A'\cup B=B\), which of the following conclusions is correct?
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Answer and explanation
Correct answer: \(A'\subseteq B\)
The equality \(A'\cup B=B\) means that adding every element of \(A'\) to \(B\) does not enlarge \(B\). Therefore, every element of \(A'\) must already be an element of \(B\), so \(A'\subseteq B\). The reverse inclusion, equality of the sets, and disjointness are not forced by the given condition.
Frequently asked questions
What is the correct answer to this question?
\(A'\subseteq B\)
Why is this the correct answer?
The equality \(A'\cup B=B\) means that adding every element of \(A'\) to \(B\) does not enlarge \(B\). Therefore, every element of \(A'\) must already be an element of \(B\), so \(A'\subseteq B\). The reverse inclusion, equality of the sets, and disjointness are not forced by the given condition.
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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