If only (A\cap B) has (14), only (B\cap C) has (12), only (C\cap A) has (15), and (A\cap B\cap C) has (8) elements, then what is (n((A\cap B)\cup(B\cap C)\cup(C\cap A)))?
Advertisement
Answer and explanation
Correct answer: (49)
The union of the three pairwise intersections contains every element that belongs to at least two sets. Its disjoint Venn regions are: only A∩B with 14, only B∩C with 12, only C∩A with 15, and the central A∩B∩C region with 8. Add each once: 14+12+15+8=49.
Frequently asked questions
What is the correct answer to this question?
(49)
Why is this the correct answer?
The union of the three pairwise intersections contains every element that belongs to at least two sets. Its disjoint Venn regions are: only A∩B with 14, only B∩C with 12, only C∩A with 15, and the central A∩B∩C region with 8. Add each once: 14+12+15+8=49.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement