If n(A ∪ B) = 45, n(A) = 28, and n(B) = 25, find n(A ∩ B).
Answer and explanation
Correct answer: 8
Use the two-set inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substituting the data, n(A ∩ B) = 28 + 25 − 45 = 53 − 45 = 8. Thus option A is correct. The value 12 does not follow from the formula, 17 is an incorrect subtraction, and 53 is merely n(A) + n(B) before correcting for overlap.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Use the two-set inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substituting the data, n(A ∩ B) = 28 + 25 − 45 = 53 − 45 = 8. Thus option A is correct. The value 12 does not follow from the formula, 17 is an incorrect subtraction, and 53 is merely n(A) + n(B) before correcting for overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
