If n(A ∩ B) = 26 and n(A ∩ B ∩ C) = 10, how many elements are only in A ∩ B?
Answer and explanation
Correct answer: 16
The pairwise intersection A ∩ B includes every element common to A and B, including those also belonging to C. Therefore, the 10 elements in A ∩ B ∩ C must be removed to obtain the region only in A ∩ B. Calculation: 26 − 10 = 16. The value 26 includes the triple-overlap, while 10 counts only that central part, so neither is the requested exclusive pairwise region.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The pairwise intersection A ∩ B includes every element common to A and B, including those also belonging to C. Therefore, the 10 elements in A ∩ B ∩ C must be removed to obtain the region only in A ∩ B. Calculation: 26 − 10 = 16. The value 26 includes the triple-overlap, while 10 counts only that central part, so neither is the requested exclusive pairwise region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
