If \(U=\{x:x\in\mathbb{N},1\le x\le 30\}\) and \(A=\{x:x\text{ is divisible by }2\text{ or }3\}\), what is \(n(A^c)\)?
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Answer and explanation
Correct answer: 10
Among the integers from 1 through 30, 15 are divisible by 2 and 10 are divisible by 3. The 5 numbers divisible by both 2 and 3 were counted twice, so \(n(A)=15+10-5=20\). Since \(U\) has 30 elements, the complement contains \(n(A^c)=30-20=10\) elements. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Among the integers from 1 through 30, 15 are divisible by 2 and 10 are divisible by 3. The 5 numbers divisible by both 2 and 3 were counted twice, so \(n(A)=15+10-5=20\). Since \(U\) has 30 elements, the complement contains \(n(A^c)=30-20=10\) elements. Therefore, option A is 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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