In a Venn diagram, n(A ∩ B) = 14 and n(A ∩ B ∩ C) = 6. How many elements are only in A ∩ B?
Answer and explanation
Correct answer: 8
The quantity n(A ∩ B) = 14 includes every element common to A and B, including the elements that may also belong to C. The triple intersection A ∩ B ∩ C contains 6 of these elements. “Only in A ∩ B” means the elements common to A and B but outside C, so subtract the triple-overlap: 14 − 6 = 8. Therefore, option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The quantity n(A ∩ B) = 14 includes every element common to A and B, including the elements that may also belong to C. The triple intersection A ∩ B ∩ C contains 6 of these elements. “Only in A ∩ B” means the elements common to A and B but outside C, so subtract the triple-overlap: 14 − 6 = 8. Therefore, option A is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
