In a Venn diagram, only A has 26 elements, only B has 31, only C has 24, only A ∩ B has 14, only B ∩ C has 16, only C ∩ A has 12, and all three have 9 elements. How many elements are in exactly one set?
Answer and explanation
Correct answer: 81
“Exactly one set” means elements that belong to A only, B only, or C only. It excludes every pairwise-overlap-only region and the central region common to all three sets. Therefore add only the three single-set regions: 26 + 31 + 24 = 81. The values 14, 16, 12, and 9 describe elements in at least two sets and must not be included.
Frequently asked questions
What is the correct answer to this question?
81
Why is this the correct answer?
“Exactly one set” means elements that belong to A only, B only, or C only. It excludes every pairwise-overlap-only region and the central region common to all three sets. Therefore add only the three single-set regions: 26 + 31 + 24 = 81. The values 14, 16, 12, and 9 describe elements in at least two sets and must not be included.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
