If \(A'=B'\), what is the correct conclusion for \(A\) and \(B\)?
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Answer and explanation
Correct answer: \(A=B\)
The complement operation is reversible because the complement of a complement is the original set. Starting with \(A'=B'\), take complements on both sides: \((A')'=(B')'\). Thus \(A=B\). The other statements do not necessarily follow from equality of the complements, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The complement operation is reversible because the complement of a complement is the original set. Starting with \(A'=B'\), take complements on both sides: \((A')'=(B')'\). Thus \(A=B\). The other statements do not necessarily follow from equality of the complements, so option C 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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