If \(n(U)=31\) for the universal set \(U\), what is the value of \(n(A\cup A^c)\)?
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Answer and explanation
Correct answer: \(31\)
Every element of the universal set belongs either to \(A\) or to its complement \(A^c\). Therefore, their union covers the entire universal set: \(A\cup A^c=U\). Taking cardinalities gives \(n(A\cup A^c)=n(U)=31\). The empty set is the intersection \(A\cap A^c\), not the union, so option B is incorrect.
Frequently asked questions
What is the correct answer to this question?
\(31\)
Why is this the correct answer?
Every element of the universal set belongs either to \(A\) or to its complement \(A^c\). Therefore, their union covers the entire universal set: \(A\cup A^c=U\). Taking cardinalities gives \(n(A\cup A^c)=n(U)=31\). The empty set is the intersection \(A\cap A^c\), not the union, so option B is incorrect.
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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