If n(B) = 66 and n(A ∩ B) = 31, how many elements are only in B, that is, in B but not in A?
Answer and explanation
Correct answer: 35
The total number of elements in B includes both the elements only in B and the common elements in A ∩ B. Hence n(B only) = n(B) − n(A ∩ B) = 66 − 31 = 35. Option A is the intersection itself, not the exclusive B region. Option C is the complete size of B, and option D is an incorrect addition. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
The total number of elements in B includes both the elements only in B and the common elements in A ∩ B. Hence n(B only) = n(B) − n(A ∩ B) = 66 − 31 = 35. Option A is the intersection itself, not the exclusive B region. Option C is the complete size of B, and option D is an incorrect addition. Therefore, 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).
