Final answer:
If A union B equals B, it implies that A is a subset of B because the union of A and B would not introduce any elements not already in B. It does not imply that B is a subset of A.
Step-by-step explanation:
If we have two sets that satisfy a ∪ b = b, it does imply that a ⊆ b (A is a subset of B). This is because the union of A and B (A ∪ B) includes all elements that are in A, in B, or in both. If A ∪ B is equal to B, then every element in A must also be in B; otherwise, there would be elements in the union that are not in B, which would contradict the given that A ∪ B = B.
Therefore, it does not follow that b ⊆ a (B is a subset of A) because there is no information given that suggests every element in B is also in A. Essentially, the set B can contain all elements of A along with additional elements not found in A, which would still satisfy the condition A ∪ B = B.