If n(A)=42, n(A ∩ B)=15, n(A ∩ C)=18, and n(A ∩ B ∩ C)=7, how many elements are only in A?
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Answer and explanation
Correct answer: 16
The only-A region is calculated by n(A)−n(A ∩ B)−n(A ∩ C)+n(A ∩ B ∩ C). Hence, Only A = 42−15−18+7 = 16. The triple intersection must be added once because its elements were included in both pairwise intersections and would otherwise be subtracted twice. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The only-A region is calculated by n(A)−n(A ∩ B)−n(A ∩ C)+n(A ∩ B ∩ C). Hence, Only A = 42−15−18+7 = 16. The triple intersection must be added once because its elements were included in both pairwise intersections and would otherwise be subtracted twice. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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