Final answer:
The union of set A with the intersection of sets B and C, A∩(B∩C), results in the set {10,11,17,20,28,30,31}.
Step-by-step explanation:
The student has asked for the set resulting from the union of set A and the intersection of sets B and C, specifically A∩(B∩C). First, we must find the intersection of sets B and C. This intersection includes all elements that are common to both B and C. B = {2,11,21,28}. The intersection of B and C (B∩C) is therefore {11,28}, as these are the common elements. Next, we take the union of set A with the result of the intersection we just found.
The union consists of all unique elements that are either in set A, in B∩C, or in both. A = {10,17,20,28,30,31. Thus, the union A∩(B∩C) is {10,11,17,20,28,30,31}, which includes all unique elements from A and the intersection of B and C. To find the set A∪(B∩C), we first need to find the intersection of sets B and C. From the given sets, B∩C = {28}. Next, we take the union of set A and the intersection of sets B and C. So, A∪(B∩C) = {10, 17, 20, 28}.