If \(A=\{x\mid x\in\mathbb{N},\ x\text{ is a divisor of }9\}\) and \(B=\{1,3,9\}\), how are A and B related?
Answer and explanation
Correct answer: A and B are equal sets
The positive natural-number divisors of 9 are 1, 3, and 9. Therefore the set described by A is \(A=\{1,3,9\}\), which is exactly the given set B. Since two sets are equal when they contain precisely the same elements, A and B are equal. They are not disjoint, empty, or in a proper-subset relationship. The order in which elements are listed would not affect equality, although here the order is already the same.
Frequently asked questions
What is the correct answer to this question?
A and B are equal sets
Why is this the correct answer?
The positive natural-number divisors of 9 are 1, 3, and 9. Therefore the set described by A is \(A=\{1,3,9\}\), which is exactly the given set B. Since two sets are equal when they contain precisely the same elements, A and B are equal. They are not disjoint, empty, or in a proper-subset relationship. The order in which elements are listed would not affect equality, although here the order is already the same.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
