If \(A=U\), what is \(A^c\)?
Answer and explanation
Correct answer: \(\varnothing\)
The complement of \(A\) contains the elements of the universal set that are not in \(A\). If \(A=U\), every element of the universal set is already in \(A\), so no element remains outside it. Therefore, \(A^c=U\setminus U=\varnothing\). Notice that \(\{U\}\) would be a singleton containing the set \(U\), not the empty set.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The complement of \(A\) contains the elements of the universal set that are not in \(A\). If \(A=U\), every element of the universal set is already in \(A\), so no element remains outside it. Therefore, \(A^c=U\setminus U=\varnothing\). Notice that \(\{U\}\) would be a singleton containing the set \(U\), not 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.
