Let \(U=\{1,2,\ldots,20\}\). If \(A\) is the set of multiples of 4 and \(B\) is the set of multiples of 6 in \(U\), what is \(n((A\cup B)')\)?
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Answer and explanation
Correct answer: 13
Within \(U\), the multiples of 4 are \(\{4,8,12,16,20\}\), so \(n(A)=5\). The multiples of 6 are \(\{6,12,18\}\), so \(n(B)=3\). Their only common element is 12, giving \(n(A\cap B)=1\). By inclusion-exclusion, \(n(A\cup B)=5+3-1=7\). Therefore, the complement contains \(20-7=13\) elements, so option D is correct.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
Within \(U\), the multiples of 4 are \(\{4,8,12,16,20\}\), so \(n(A)=5\). The multiples of 6 are \(\{6,12,18\}\), so \(n(B)=3\). Their only common element is 12, giving \(n(A\cap B)=1\). By inclusion-exclusion, \(n(A\cup B)=5+3-1=7\). Therefore, the complement contains \(20-7=13\) elements, so option D is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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