If n(A ∪ B) = 54, n(A \ B) = 17, and n(B \ A) = 21, what is n(A ∩ B)?
Answer and explanation
Correct answer: 16
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A \ B) + n(B \ A) + n(A ∩ B). Substituting the values gives 54 = 17 + 21 + n(A ∩ B), so n(A ∩ B) = 54 − 38 = 16. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The union A ∪ B consists of three mutually disjoint regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A \ B) + n(B \ A) + n(A ∩ B). Substituting the values gives 54 = 17 + 21 + n(A ∩ B), so n(A ∩ B) = 54 − 38 = 16. Hence, option A 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).
