If n(A) = 64, n(B) = 59, n(A − B) = 22, and n(B − A) = 20, what is the correct conclusion about the data?
Answer and explanation
Correct answer: The data are inconsistent.
For set A, the intersection would have size n(A) − n(A − B) = 64 − 22 = 42. For set B, it would have size n(B) − n(B − A) = 59 − 20 = 39. The same intersection cannot simultaneously have two different cardinalities. Therefore the supplied data are inconsistent, making option A correct; the other conclusions do not resolve this contradiction.
Frequently asked questions
What is the correct answer to this question?
The data are inconsistent.
Why is this the correct answer?
For set A, the intersection would have size n(A) − n(A − B) = 64 − 22 = 42. For set B, it would have size n(B) − n(B − A) = 59 − 20 = 39. The same intersection cannot simultaneously have two different cardinalities. Therefore the supplied data are inconsistent, making option A correct; the other conclusions do not resolve this contradiction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
