If the universal set \(U\) has \(n(U)=48\) and the complement of set \(A\) has \(n(A^c)=19\), what is the value of \(n(A)\)?
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Answer and explanation
Correct answer: 29
For a finite universal set, the set \(A\) and its complement \(A^c\) are disjoint and together contain every element of \(U\). Therefore, their cardinalities satisfy \(n(A)+n(A^c)=n(U)\). Substituting the given values gives \(n(A)+19=48\), so \(n(A)=48-19=29\). Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
For a finite universal set, the set \(A\) and its complement \(A^c\) are disjoint and together contain every element of \(U\). Therefore, their cardinalities satisfy \(n(A)+n(A^c)=n(U)\). Substituting the given values gives \(n(A)+19=48\), so \(n(A)=48-19=29\). 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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