If \(n(U)=30\) and \(n(A)=18\), what is the value of \(n(A')\)?
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Answer and explanation
Correct answer: 12
For a finite universal set, the set \(A\) and its complement \(A'\) are disjoint and together contain all elements of \(U\). Therefore, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Substituting the given values gives \(18+n(A')=30\), so \(n(A')=30-18=12\). Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
For a finite universal set, the set \(A\) and its complement \(A'\) are disjoint and together contain all elements of \(U\). Therefore, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Substituting the given values gives \(18+n(A')=30\), so \(n(A')=30-18=12\). Thus, option A 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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