If U = {1, 2, ..., 30}, A = {x : x ∈ U, 2 divides x}, and B = {x : x ∈ U, 5 divides x}, then what is n(A \ B)?
Advertisement
Answer and explanation
Correct answer: 12
Set A contains the even numbers from 1 to 30, so n(A) = 30/2 = 15. The elements that belong to both A and B must be divisible by both 2 and 5, hence they are multiples of 10: 10, 20, and 30. Thus n(A ∩ B) = 3. Removing these from A gives n(A \ B) = 15 − 3 = 12. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Set A contains the even numbers from 1 to 30, so n(A) = 30/2 = 15. The elements that belong to both A and B must be divisible by both 2 and 5, hence they are multiples of 10: 10, 20, and 30. Thus n(A ∩ B) = 3. Removing these from A gives n(A \ B) = 15 − 3 = 12. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement