Final answer:
It is not possible to find sets A and B such that |A| = 4, |B| = 5, and |A ∩ B| = 9 because an intersection cannot contain more elements than the smallest set involved.
Step-by-step explanation:
The student is asking about the relationship between two sets A and B and their intersection. More specifically, they have asked for an example where set A has 4 elements (|A| = 4), set B has 5 elements (|B| = 5), and the intersection of A and B (A ∩ B) has 9 elements. However, it is not possible for the intersection of two sets to have more elements than either of the individual sets. This is because the intersection consists of only those elements that are common to both sets.
Sets A and B cannot have an intersection with more elements than the set with the fewest elements. If |A| = 4 and |B| = 5, the biggest possible size for A ∩ B would be 4, assuming all elements of A are also in B. Hence, there cannot exist sets A and B such that |A ∩ B| = 9 with the given sizes for A and B.