Let U = {1, 2, 3, ..., 100}. A is the set of numbers divisible by 2, B the set of numbers divisible by 5, and C the set of numbers divisible by 10. Which relation is correct?
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Answer and explanation
Correct answer: C = A ∩ B
A number is divisible by 10 exactly when it is divisible by both 2 and 5, because 10 = 2 × 5 and these factors are coprime. Thus the numbers common to A and B are precisely the numbers in C. Therefore, C = A ∩ B. For example, 10, 20, and 30 belong to all three sets, whereas 2 belongs to A but not to C.
Frequently asked questions
What is the correct answer to this question?
C = A ∩ B
Why is this the correct answer?
A number is divisible by 10 exactly when it is divisible by both 2 and 5, because 10 = 2 × 5 and these factors are coprime. Thus the numbers common to A and B are precisely the numbers in C. Therefore, C = A ∩ B. For example, 10, 20, and 30 belong to all three sets, whereas 2 belongs to A but not to C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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