If \(U=\{1,2,\ldots,60\}\), \(A=\{x:x\text{ is divisible by }6\}\), and \(B=\{x:x\text{ is divisible by }10\}\), what is \(|(A\cap B)'|\)?
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Answer and explanation
Correct answer: 58
An element belongs to both \(A\) and \(B\) exactly when it is divisible by both 6 and 10. Such numbers are multiples of \(\operatorname{lcm}(6,10)=30\). Within \(1\) to \(60\), these are 30 and 60, so \(|A\cap B|=2\). Therefore \(|(A\cap B)'|=60-2=58\).
Frequently asked questions
What is the correct answer to this question?
58
Why is this the correct answer?
An element belongs to both \(A\) and \(B\) exactly when it is divisible by both 6 and 10. Such numbers are multiples of \(\operatorname{lcm}(6,10)=30\). Within \(1\) to \(60\), these are 30 and 60, so \(|A\cap B|=2\). Therefore \(|(A\cap B)'|=60-2=58\).
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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