If n(A ∪ B) = 70, n(A) = 46, n(B) = 35, and n(B \ A) = 24, what is n(A ∩ B)?
Answer and explanation
Correct answer: 11
Set B is partitioned into two disjoint parts: the elements of B that are outside A, namely B \ A, and the elements common to both sets, namely A ∩ B. Thus n(B) = n(B \ A) + n(A ∩ B). Substituting the given values gives 35 = 24 + n(A ∩ B), so n(A ∩ B) = 35 − 24 = 11. Hence option A is correct; the union and n(A) values are unnecessary for this calculation.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
Set B is partitioned into two disjoint parts: the elements of B that are outside A, namely B \ A, and the elements common to both sets, namely A ∩ B. Thus n(B) = n(B \ A) + n(A ∩ B). Substituting the given values gives 35 = 24 + n(A ∩ B), so n(A ∩ B) = 35 − 24 = 11. Hence option A is correct; the union and n(A) values are unnecessary for this calculation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
