Final answer:
The set A consists of the union of elements from A - B and A ∩ B, resulting in Set A = {1, 3, 5, 6, 7, 8, 9}. Set B is the union of B - A and A ∩ B, giving Set B = {2, 3, 6, 9, 10}.
Step-by-step explanation:
To find the sets A and B, we consider the given information: A - B = {1, 5, 7, 8}, B - A = {2, 10}, and A ∩ B = {3, 6, 9}. The set A - B consists of elements that are in A but not in B. Similarly, B - A contains elements that are in B but not in A. The set A ∩ B contains elements that are in both sets A and B.
Combining the elements from A - B and A ∩ B gives us all the elements in set A, because A is the union of the elements unique to A and the elements in both A and B. Hence, Set A = {1, 5, 7, 8} ∪ {3, 6, 9} = {1, 3, 5, 6, 7, 8, 9}.
To find set B, we combine the elements from B - A and A ∩ B. Therefore, Set B = {2, 10} ∪ {3, 6, 9} = {2, 3, 6, 9, 10}.
We can now clearly see the full composition of sets A and B based on the subtraction and intersection operations provided.