Final answer:
To find set B given that B is a subset of A, and given AnB and AuB, we deduce that B must be equal to AnB, so B = {1,4,5}.
Step-by-step explanation:
Given that B is a subset of A, and you have the information that AnB = {1,4,5} and AuB = {1,2,3,4,5,6}, you can find set B. Since AnB contains all elements that are in both A and B, and because B is a subset of A, all elements in B must be in AnB.
Therefore, considering the given AuB, which contains all elements in A or B or both, we can conclude that since B does not contribute any new elements to AuB than those already in AnB, Set B must be equal to AnB.
Thus, set B = {1,4,5}.