If only A has 12, only B has 15, only C has 10, exactly two has 33, all three has 9, and outside has 21, what is n(U)?
Answer and explanation
Correct answer: 100
A universal set contains every region shown in the Venn diagram, including elements in exactly one set, elements in exactly two sets, elements in all three sets, and elements outside all three sets. Therefore n(U)=12+15+10+33+9+21=100. No region should be omitted because the outside region is also part of the universal set. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
A universal set contains every region shown in the Venn diagram, including elements in exactly one set, elements in exactly two sets, elements in all three sets, and elements outside all three sets. Therefore n(U)=12+15+10+33+9+21=100. No region should be omitted because the outside region is also part of the universal set. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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