If \(U=\{1,2,\ldots,72\}\), \(A\) is the set of multiples of 4, and \(B\) is the set of multiples of 9, what is \(|(A\cup B)'|\)?
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Answer and explanation
Correct answer: 48
There are \(72/4=18\) multiples of 4 and \(72/9=8\) multiples of 9. Numbers counted in both sets are multiples of \(\operatorname{lcm}(4,9)=36\); these are 36 and 72, so there are 2. Thus \(|A\cup B|=18+8-2=24\). The complement within a 72-element universal set has \(72-24=48\) elements.
Frequently asked questions
What is the correct answer to this question?
48
Why is this the correct answer?
There are \(72/4=18\) multiples of 4 and \(72/9=8\) multiples of 9. Numbers counted in both sets are multiples of \(\operatorname{lcm}(4,9)=36\); these are 36 and 72, so there are 2. Thus \(|A\cup B|=18+8-2=24\). The complement within a 72-element universal set has \(72-24=48\) elements.
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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