If \(A=\varnothing\) and the universal set is \(U\), what is \(A^c\)?
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Answer and explanation
Correct answer: \(U\)
The empty set contains no elements, so there is no element of \(U\) to remove when forming its complement. By definition, \(A^c=U\setminus A\). With \(A=\varnothing\), this becomes \(\varnothing^c=U\setminus\varnothing=U\). Thus, the entire universal set is the complement of the empty set.
Frequently asked questions
What is the correct answer to this question?
\(U\)
Why is this the correct answer?
The empty set contains no elements, so there is no element of \(U\) to remove when forming its complement. By definition, \(A^c=U\setminus A\). With \(A=\varnothing\), this becomes \(\varnothing^c=U\setminus\varnothing=U\). Thus, the entire universal set is the complement of the empty set.
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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