If \(n(U)=30\) and \(n(A)=11\), what is \(n(A')\)?
Answer and explanation
Correct answer: 19
The complement \(A'\) contains all elements of the universal set \(U\) that are not in \(A\). Therefore, its cardinality is found by subtracting the number of elements in \(A\) from the number in \(U\): \(n(A')=n(U)-n(A)=30-11=19\). Thus, option B is correct. The other options either give the size of \(A\), the size of \(U\), or an incorrect sum.
Frequently asked questions
What is the correct answer to this question?
19
Why is this the correct answer?
The complement \(A'\) contains all elements of the universal set \(U\) that are not in \(A\). Therefore, its cardinality is found by subtracting the number of elements in \(A\) from the number in \(U\): \(n(A')=n(U)-n(A)=30-11=19\). Thus, option B is correct. The other options either give the size of \(A\), the size of \(U\), or an incorrect sum.
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.
