Let A = {x : x is a positive natural number, x ≤ 15, and 2 divides x} and B = {x : x is a positive natural number, x ≤ 15, and 5 divides x}. How many elements are in A ∪ B?
Answer and explanation
Correct answer: 9
The elements of A are the positive multiples of 2 not exceeding 15: {2, 4, 6, 8, 10, 12, 14}, so n(A) = 7. The elements of B are {5, 10, 15}, so n(B) = 3. The common element is 10, hence n(A ∩ B) = 1. By the inclusion–exclusion formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 7 + 3 − 1 = 9. The common element must not be counted twice.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The elements of A are the positive multiples of 2 not exceeding 15: {2, 4, 6, 8, 10, 12, 14}, so n(A) = 7. The elements of B are {5, 10, 15}, so n(B) = 3. The common element is 10, hence n(A ∩ B) = 1. By the inclusion–exclusion formula, n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 7 + 3 − 1 = 9. The common element must not be counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
