If \(A=\{x:x\text{ is a multiple of }4,\ 1\le x\le25\}\) and \(B=\{x:x\text{ is a multiple of }6,\ 1\le x\le25\}\), how many elements are in \(A\cup B\)?
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Answer and explanation
Correct answer: 8
The multiples of 4 up to 25 are \(\{4,8,12,16,20,24\}\), so \(|A|=6\). The multiples of 6 are \(\{6,12,18,24\}\), so \(|B|=4\). Their common elements are \(\{12,24\}\), giving \(|A\cap B|=2\). By inclusion–exclusion, \(|A\cup B|=6+4-2=8\). The subtraction prevents 12 and 24 from being counted twice.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The multiples of 4 up to 25 are \(\{4,8,12,16,20,24\}\), so \(|A|=6\). The multiples of 6 are \(\{6,12,18,24\}\), so \(|B|=4\). Their common elements are \(\{12,24\}\), giving \(|A\cap B|=2\). By inclusion–exclusion, \(|A\cup B|=6+4-2=8\). The subtraction prevents 12 and 24 from being counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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