If \(A=\{x\mid x\text{ is a positive multiple of }6\text{ less than }30\}\) and \(B=\{6,12,18,24\}\), which statement is correct?
Answer and explanation
Correct answer: \(A=B\)
The positive multiples of 6 that are less than 30 are obtained by using 6, 12, 18, and 24. The next multiple is 30, but it is excluded because the condition says less than 30, not less than or equal to 30. Therefore \(A=\{6,12,18,24\}=B\), so option A is correct. Options B and C incorrectly claim a proper-subset relation, while option D is false because 30 is not included.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The positive multiples of 6 that are less than 30 are obtained by using 6, 12, 18, and 24. The next multiple is 30, but it is excluded because the condition says less than 30, not less than or equal to 30. Therefore \(A=\{6,12,18,24\}=B\), so option A is correct. Options B and C incorrectly claim a proper-subset relation, while option D is false because 30 is not included.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
