Given \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\), and \(B=\{1,2,3,5,7\}\), what is \(A\cap B\)?
Answer and explanation
Correct answer: \(\{2\}\)
The intersection of two sets consists only of elements present in both sets. Comparing A = {2,4,6,8,10} with B = {1,2,3,5,7}, the only common element is 2. Therefore, \(A\cap B=\{2\}\). The other even elements belong only to A, while 1, 3, 5, and 7 belong only to B, so they cannot be included in the intersection.
Frequently asked questions
What is the correct answer to this question?
\(\{2\}\)
Why is this the correct answer?
The intersection of two sets consists only of elements present in both sets. Comparing A = {2,4,6,8,10} with B = {1,2,3,5,7}, the only common element is 2. Therefore, \(A\cap B=\{2\}\). The other even elements belong only to A, while 1, 3, 5, and 7 belong only to B, so they cannot be included 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).
