If \(n(U)=38\) and \(n(A)=16\), what is \(n(A')\)?
Answer and explanation
Correct answer: 22
The complement \(A'\) contains all elements of the universal set \(U\) that are not in \(A\). Thus, for a finite universal set, \(n(A')=n(U)-n(A)\). Substituting the given values gives \(n(A')=38-16=22\). Therefore, option B is correct. The number 16 is the size of A itself, 38 is the size of the whole universal set, and 54 incorrectly adds the two quantities instead of finding the elements outside A.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The complement \(A'\) contains all elements of the universal set \(U\) that are not in \(A\). Thus, for a finite universal set, \(n(A')=n(U)-n(A)\). Substituting the given values gives \(n(A')=38-16=22\). Therefore, option B is correct. The number 16 is the size of A itself, 38 is the size of the whole universal set, and 54 incorrectly adds the two quantities instead of finding the elements outside A.
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.
