If \(U=\{x\in\mathbb{N}\mid 1\le x\le 50\}\) and \(A=\{x\in U\mid 5\mid x\}\), what is the value of \(n(A^c)\)?
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Answer and explanation
Correct answer: 40
The universal set contains the 50 natural numbers from 1 to 50. Its elements divisible by 5 are \(5,10,15,20,25,30,35,40,45,50\), so \(n(A)=10\). A and its complement partition U, meaning \(n(U)=n(A)+n(A^c)\). Therefore, \(n(A^c)=50-10=40\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
The universal set contains the 50 natural numbers from 1 to 50. Its elements divisible by 5 are \(5,10,15,20,25,30,35,40,45,50\), so \(n(A)=10\). A and its complement partition U, meaning \(n(U)=n(A)+n(A^c)\). Therefore, \(n(A^c)=50-10=40\), making option A 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.
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