Final answer:
The number of elements in the set n[A∪(C∩B)] cannot be definitively determined without more information about the specific elements in sets C and B. However, at minimum, set A would contribute two elements to the union.
Step-by-step explanation:
The student is asking about the number of elements in the union of two sets, specifically n[A∪(C∩B)]. To solve this, we need to find the intersection of sets C and B first, which is C∩B. Since no elements are given for sets C and B, we cannot determine their intersection explicitly; however, B has the elements {2,3}. The intersection of C and B would therefore have to be either 2, 3, or both 2 and 3, since these are the only elements given in set B that could intersect with C.
Without knowing which (if any) of 2 and 3 are in C, we cannot determine the exact elements of C∩B, and thus cannot accurately calculate n[A∪(C∩B)]. However, since A = {1,2}, we can say at minimum, set A would contribute to the union, leading to at least two elements from A.
If we assume that the intersection C∩B contributes no new elements to the union beyond what is already present in A (because without specific elements, we cannot assert that C contributes any elements not already in A), then n[A∪(C∩B)] would have at least 2 elements from A, hence option B) 2 could be a potential answer. But since we cannot complete the intersection without further information, we cannot definitively conclude the exact value of n[A∪(C∩B)]