If n(A) = 55, n(B) = 50, n(A − B) = 20, and n(B − A) = 18, what is the correct conclusion about the given data?
Answer and explanation
Correct answer: The data are inconsistent
Use the partition of each set into its exclusive part and common part. From A, n(A ∩ B) = n(A) − n(A − B) = 55 − 20 = 35. From B, the same intersection must be n(B) − n(B − A) = 50 − 18 = 32. A single intersection cannot simultaneously have two different cardinalities, so the supplied figures cannot describe valid sets together. Therefore the data are inconsistent.
Frequently asked questions
What is the correct answer to this question?
The data are inconsistent
Why is this the correct answer?
Use the partition of each set into its exclusive part and common part. From A, n(A ∩ B) = n(A) − n(A − B) = 55 − 20 = 35. From B, the same intersection must be n(B) − n(B − A) = 50 − 18 = 32. A single intersection cannot simultaneously have two different cardinalities, so the supplied figures cannot describe valid sets together. Therefore the data are inconsistent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
