If \(U=\{1,2,\ldots,35\}\), \(A=\{x\in U:5\mid x\}\), and \(B=\{x\in U:x\text{ is odd}\}\), what is \(B'\cap A\)?
Answer and explanation
Correct answer: \(\{10,20,30\}\)
Within the given universal set, \(B\) consists of all odd numbers. Therefore, \(B'\) consists of all even numbers from 1 through 35. The multiples of 5 in \(A\) are \(5,10,15,20,25,30,35\). Selecting only the even members of this list gives \(10,20,30\). Hence \(B'\cap A=\{10,20,30\}\), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{10,20,30\}\)
Why is this the correct answer?
Within the given universal set, \(B\) consists of all odd numbers. Therefore, \(B'\) consists of all even numbers from 1 through 35. The multiples of 5 in \(A\) are \(5,10,15,20,25,30,35\). Selecting only the even members of this list gives \(10,20,30\). Hence \(B'\cap A=\{10,20,30\}\), 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.
