If n(A) = 35, n(B) = 27, and n(A ∪ B) = 50, what is n(A − B)?
Answer and explanation
Correct answer: 23
Use the inclusion–exclusion formula first: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence 50 = 35 + 27 − n(A ∩ B), so n(A ∩ B) = 12. The set A is made up of the disjoint parts A − B and A ∩ B. Therefore n(A − B) = n(A) − n(A ∩ B) = 35 − 12 = 23. Option B is the intersection size, not the difference size; the other values do not satisfy the given relationships.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
Use the inclusion–exclusion formula first: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Hence 50 = 35 + 27 − n(A ∩ B), so n(A ∩ B) = 12. The set A is made up of the disjoint parts A − B and A ∩ B. Therefore n(A − B) = n(A) − n(A ∩ B) = 35 − 12 = 23. Option B is the intersection size, not the difference size; the other values do not satisfy the given relationships.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
