If n(A ∩ B)=14 and n(A ∩ B ∩ C)=5, how many elements are in A and B but not in C?
Answer and explanation
Correct answer: 9
The set A ∩ B includes all elements common to A and B, including those that may also belong to C. The requested part excludes C, so remove the triple intersection: n((A ∩ B) − C) = n(A ∩ B) − n(A ∩ B ∩ C) = 14 − 5 = 9. Therefore option A is correct. The value 5 counts the part inside all three sets, not the required exclusive pairwise region.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The set A ∩ B includes all elements common to A and B, including those that may also belong to C. The requested part excludes C, so remove the triple intersection: n((A ∩ B) − C) = n(A ∩ B) − n(A ∩ B ∩ C) = 14 − 5 = 9. Therefore option A is correct. The value 5 counts the part inside all three sets, not the required exclusive pairwise region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
