If \(A=\{x\mid x\) is an even positive divisor of 24\}, which option is a subset of \(A\)?
Answer and explanation
Correct answer: \(\{2,6,8\}\)
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Selecting only the even divisors gives \(A=\{2,4,6,8,12,24\}\). Every element of \(\{2,6,8\}\) belongs to this set, so it is a subset of \(A\). Each other option contains at least one element that is not in \(A\): 1 or 3, 5, or 9. Therefore option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
\(\{2,6,8\}\)
Why is this the correct answer?
The positive divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Selecting only the even divisors gives \(A=\{2,4,6,8,12,24\}\). Every element of \(\{2,6,8\}\) belongs to this set, so it is a subset of \(A\). Each other option contains at least one element that is not in \(A\): 1 or 3, 5, or 9. Therefore option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
