If n(A) = 20, n(B) = 15, and n(A ∪ B) = 28, what is n(A ∩ B)?
Answer and explanation
Correct answer: 7
Use the inclusion–exclusion identity n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution yields n(A ∩ B) = 20 + 15 − 28 = 7. The intersection therefore contains 7 elements. This subtraction prevents the elements common to both sets from being counted twice in the sum n(A) + n(B). Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Use the inclusion–exclusion identity n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution yields n(A ∩ B) = 20 + 15 − 28 = 7. The intersection therefore contains 7 elements. This subtraction prevents the elements common to both sets from being counted twice in the sum n(A) + n(B). Hence option B 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).
