If \(n(U)=72\) and \(n(A)=29\), what is \(n(A')\)?
Answer and explanation
Correct answer: 43
The complement \(A'\) consists of all elements in the universal set \(U\) that are not in \(A\). Since \(A\) and \(A'\) together partition \(U\), their cardinalities satisfy \(n(A')=n(U)-n(A)\). Substitution gives \(72-29=43\). Therefore, option B is correct. The value 29 is the size of A itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
The complement \(A'\) consists of all elements in the universal set \(U\) that are not in \(A\). Since \(A\) and \(A'\) together partition \(U\), their cardinalities satisfy \(n(A')=n(U)-n(A)\). Substitution gives \(72-29=43\). Therefore, option B is correct. The value 29 is the size of A itself, not its complement.
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.
