If \(A\subseteq U\) and \(A'=\varnothing\), which conclusion is correct?
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Answer and explanation
Correct answer: \(A=U\)
The complement is defined by \(A'=U\setminus A\). If \(A'=\varnothing\), then there is no element of \(U\) outside \(A\); hence every element of \(U\) belongs to \(A\), so \(U\subseteq A\). Since the question already gives \(A\subseteq U\), both inclusions imply \(A=U\). Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=U\)
Why is this the correct answer?
The complement is defined by \(A'=U\setminus A\). If \(A'=\varnothing\), then there is no element of \(U\) outside \(A\); hence every element of \(U\) belongs to \(A\), so \(U\subseteq A\). Since the question already gives \(A\subseteq U\), both inclusions imply \(A=U\). Therefore option B 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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