If n(A)=50, n(A∩B)=21, n(A∩C)=19, and n(A∩B∩C)=8, how many elements are only in A, that is, in A but not in B or C?
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Answer and explanation
Correct answer: 18
To count elements only in A, begin with all 50 elements of A. Subtract the 21 elements shared by A and B and the 19 shared by A and C. The 8 elements in all three sets were subtracted twice, so add them back once: 50−21−19+8=18. Therefore, 18 elements are in A but in neither B nor C.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
To count elements only in A, begin with all 50 elements of A. Subtract the 21 elements shared by A and B and the 19 shared by A and C. The 8 elements in all three sets were subtracted twice, so add them back once: 50−21−19+8=18. Therefore, 18 elements are in A but in neither B nor C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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