If \(U=\{1,2,\ldots,27\}\), \(A=\{x\in U:3\mid x\}\), and \(B=\{x\in U:9\mid x\}\), what is \(A\cap B'\)?
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Answer and explanation
Correct answer: \(\{3,6,12,15,21,24\}\)
The set \(A\) contains all multiples of 3 in \(U\): \(\{3,6,9,12,15,18,21,24,27\}\). The set \(B\) contains the multiples of 9: \(\{9,18,27\}\). Thus \(B'\) excludes exactly these three numbers. Removing them from A leaves \(\{3,6,12,15,21,24\}\). Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{3,6,12,15,21,24\}\)
Why is this the correct answer?
The set \(A\) contains all multiples of 3 in \(U\): \(\{3,6,9,12,15,18,21,24,27\}\). The set \(B\) contains the multiples of 9: \(\{9,18,27\}\). Thus \(B'\) excludes exactly these three numbers. Removing them from A leaves \(\{3,6,12,15,21,24\}\). 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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