If \(U=\{1,2,\ldots,50\}\) and \(A=\{x\in U:5\mid x\}\), what is the value of \(n(A')\)?
Answer and explanation
Correct answer: 40
The set \(A\) contains the positive multiples of 5 from 1 through 50: \(5,10,15,20,25,30,35,40,45,50\). There are \(50/5=10\) such multiples, so \(n(A)=10\). The universal set has 50 elements. Since \(A'\) contains all elements of \(U\) that are not in \(A\), its cardinality is \(n(A')=n(U)-n(A)=50-10=40\). Therefore option A is correct; 10 is the cardinality of A itself.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The set \(A\) contains the positive multiples of 5 from 1 through 50: \(5,10,15,20,25,30,35,40,45,50\). There are \(50/5=10\) such multiples, so \(n(A)=10\). The universal set has 50 elements. Since \(A'\) contains all elements of \(U\) that are not in \(A\), its cardinality is \(n(A')=n(U)-n(A)=50-10=40\). Therefore option A is correct; 10 is the cardinality of A itself.
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.
