If, for a universal set \(U\), \(n(A)=15\) and \(n(A')=35\), what is \(n(U)\)?
Advertisement
Answer and explanation
Correct answer: 50
The set \(A\) and its complement \(A'\) are disjoint, and every element of the universal set belongs to exactly one of them. Hence, \(A\cup A'=U\) and \(n(U)=n(A)+n(A')\). Substituting the given values gives \(n(U)=15+35=50\). Therefore, the universal set contains 50 elements, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
The set \(A\) and its complement \(A'\) are disjoint, and every element of the universal set belongs to exactly one of them. Hence, \(A\cup A'=U\) and \(n(U)=n(A)+n(A')\). Substituting the given values gives \(n(U)=15+35=50\). Therefore, the universal set contains 50 elements, so 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.
Advertisement