If \(U=\{1,2,\ldots,16\}\), \(A=\{1,4,9,16\}\), and \(B=\{2,4,6,8,10,12,14,16\}\), what is \(A\cap B'\)?
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Answer and explanation
Correct answer: \(\{1,9\}\)
The complement \(B'\), relative to \(U\), contains the elements not listed in \(B\); here these are the odd numbers from 1 to 15. From \(A=\{1,4,9,16\}\), the elements that are not in \(B\) are 1 and 9. Hence \(A\cap B'=\{1,9\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{1,9\}\)
Why is this the correct answer?
The complement \(B'\), relative to \(U\), contains the elements not listed in \(B\); here these are the odd numbers from 1 to 15. From \(A=\{1,4,9,16\}\), the elements that are not in \(B\) are 1 and 9. Hence \(A\cap B'=\{1,9\}\), so 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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