If \(A=\{5,10,15\}\) and \(B=\{x\mid x\text{ is a positive multiple of }5\text{ less than }20\}\), what is the relation between A and B?
Answer and explanation
Correct answer: \(A=B\)
The positive multiples of 5 below 20 are 5, 10, and 15. The number 20 is not included because the inequality is strict: less than 20. Hence the set described by B is \(\{5,10,15\}\), exactly the same as A. Therefore A and B are equal sets, and option A is correct. Neither proper-subset option applies, and option D is false because 20 is excluded from B.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The positive multiples of 5 below 20 are 5, 10, and 15. The number 20 is not included because the inequality is strict: less than 20. Hence the set described by B is \(\{5,10,15\}\), exactly the same as A. Therefore A and B are equal sets, and option A is correct. Neither proper-subset option applies, and option D is false because 20 is excluded from B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
