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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10

Let U = {1, 2, ..., 50}, A = {x ∈ U | 2 divides x}, and B = {x ∈ U | 5 divides x}. How many elements are in A \ B?

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Answer and explanation

Correct answer: 20

Set A consists of the even numbers from 1 through 50, so it has 50 ÷ 2 = 25 elements. Elements in both A and B must be divisible by both 2 and 5, hence divisible by 10. There are 50 ÷ 10 = 5 such elements. Therefore, A \ B contains the even numbers that are not divisible by 5, and its size is 25 − 5 = 20.

Tags

setsset differencedivisibilitycountingOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

20

Why is this the correct answer?

Set A consists of the even numbers from 1 through 50, so it has 50 ÷ 2 = 25 elements. Elements in both A and B must be divisible by both 2 and 5, hence divisible by 10. There are 50 ÷ 10 = 5 such elements. Therefore, A \ B contains the even numbers that are not divisible by 5, and its size is 25 − 5 = 20.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

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