If \(A=\{2,5,10\}\) and \(B=\{5,10,15\}\), which of the following sets is a subset of \(A\cap B\)?
Answer and explanation
Correct answer: \(\{5\}\)
The intersection contains elements common to both sets. Comparing \(A\) and \(B\), we obtain \(A\cap B=\{5,10\}\). A set is a subset of another set when every element of the first set is contained in the second set. Since the only element of \(\{5\}\) is 5, and 5 belongs to \(\{5,10\}\), option A is correct. The other options contain 2 or 15, which are not in the intersection.
Frequently asked questions
What is the correct answer to this question?
\(\{5\}\)
Why is this the correct answer?
The intersection contains elements common to both sets. Comparing \(A\) and \(B\), we obtain \(A\cap B=\{5,10\}\). A set is a subset of another set when every element of the first set is contained in the second set. Since the only element of \(\{5\}\) is 5, and 5 belongs to \(\{5,10\}\), option A is correct. The other options contain 2 or 15, which are not in the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
