If \(n(U)=80\) and \(n(A')=19\), what is \(n(A)\)?
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Answer and explanation
Correct answer: 61
A set and its complement are disjoint and together contain every element of the universal set. Therefore, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Substituting the given values gives \(n(A)+19=80\), so \(n(A)=80-19=61\). Hence option C is correct. The answer cannot exceed 80 because \(A\subseteq U\).
Frequently asked questions
What is the correct answer to this question?
61
Why is this the correct answer?
A set and its complement are disjoint and together contain every element of the universal set. Therefore, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Substituting the given values gives \(n(A)+19=80\), so \(n(A)=80-19=61\). Hence option C is correct. The answer cannot exceed 80 because \(A\subseteq U\).
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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