If only A∩B has 19 elements, only B∩C has 17 elements, only C∩A has 21 elements, and A∩B∩C has 11 elements, how many elements are in at least two sets?
Answer and explanation
Correct answer: 68
The phrase “at least two sets” includes every element lying in exactly two sets as well as every element lying in all three sets. The relevant Venn regions are therefore the three pairwise-only regions and the central triple-intersection region. Adding them gives 19 + 17 + 21 + 11 = 68. The central region is included only once because each element must be counted once.
Frequently asked questions
What is the correct answer to this question?
68
Why is this the correct answer?
The phrase “at least two sets” includes every element lying in exactly two sets as well as every element lying in all three sets. The relevant Venn regions are therefore the three pairwise-only regions and the central triple-intersection region. Adding them gives 19 + 17 + 21 + 11 = 68. The central region is included only once because each element must be counted once.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
