If the complement of \(A\) with respect to the universal set \(U\) is \(A'=\varnothing\), which statement about \(A\) is correct?
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Answer and explanation
Correct answer: \(A=U\)
The complement is defined by \(A'=U\setminus A\), so it contains the elements of \(U\) that are outside \(A\). If this complement is empty, no element of \(U\) lies outside \(A\). Since \(A\) is a subset of \(U\), it must contain every element of \(U\), and therefore \(A=U\).
Frequently asked questions
What is the correct answer to this question?
\(A=U\)
Why is this the correct answer?
The complement is defined by \(A'=U\setminus A\), so it contains the elements of \(U\) that are outside \(A\). If this complement is empty, no element of \(U\) lies outside \(A\). Since \(A\) is a subset of \(U\), it must contain every element of \(U\), and therefore \(A=U\).
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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