If n(A) = 25, n(B) = 18 and n(A ∩ B) = 10, how many elements are only in A?
Answer and explanation
Correct answer: 15
The set A includes two parts: the elements only in A and the elements common to both A and B. Thus, n(A) = n(A only) + n(A ∩ B). Rearranging gives n(A only) = n(A) − n(A ∩ B) = 25 − 10 = 15. Therefore, option C is correct. The value 10 represents the common intersection, not the part belonging exclusively to A.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The set A includes two parts: the elements only in A and the elements common to both A and B. Thus, n(A) = n(A only) + n(A ∩ B). Rearranging gives n(A only) = n(A) − n(A ∩ B) = 25 − 10 = 15. Therefore, option C is correct. The value 10 represents the common intersection, not the part belonging exclusively to A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
