If \(U'=\varnothing\), which statement about \(U\) is correct?
Answer and explanation
Correct answer: \(U\) is the universal set
The complement of a set is taken with respect to the universal set. Every element of the universal set belongs to \(U\), so there is no element left outside it; consequently, the complement of the universal set is empty: \(U'=\varnothing\). Thus the given statement identifies \(U\) as the universal set. The other options are not generally implied.
Frequently asked questions
What is the correct answer to this question?
\(U\) is the universal set
Why is this the correct answer?
The complement of a set is taken with respect to the universal set. Every element of the universal set belongs to \(U\), so there is no element left outside it; consequently, the complement of the universal set is empty: \(U'=\varnothing\). Thus the given statement identifies \(U\) as the universal set. The other options are not generally implied.
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.
