If n(A∩B)=29 and n(A∩B∩C)=12, how many elements are only in A and B but not in C?
Answer and explanation
Correct answer: 17
The set A∩B includes every element common to A and B, including those that may also lie in C. Therefore it consists of the region only in A and B together with the triple intersection A∩B∩C. To isolate the first region, subtract the triple intersection: 29−12 = 17. Option B counts the entire pairwise intersection, and option D counts only the triple part. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The set A∩B includes every element common to A and B, including those that may also lie in C. Therefore it consists of the region only in A and B together with the triple intersection A∩B∩C. To isolate the first region, subtract the triple intersection: 29−12 = 17. Option B counts the entire pairwise intersection, and option D counts only the triple part. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
