3. Find the sets A and B if A − B = {1, 5, 7, 8}, B − A = {2, 10}, and A ∩ B = {3, 6, 9}.

To find the sets A and B, we need to understand the operations given in the problem.

1. A - B = {1, 5, 7, 8} means these are the elements that are in A but not in B.
2. B - A = {2, 10} means these are the elements that are in B but not in A.
3. A ∩ B = {3, 6, 9} means these are the elements that are common to both A and B.

Now, we can find the sets A and B by combining these results.

Set A is the union of A - B and A ∩ B, which means we combine the elements of these two sets. So, A = {1, 5, 7, 8} ∪ {3, 6, 9} = {1, 3, 5, 6, 7, 8, 9}.

Set B is the union of B - A and A ∩ B, which means we combine the elements of these two sets. So, B = {2, 10} ∪ {3, 6, 9} = {2, 3, 6, 9, 10}.

So, the sets A and B are A = {1, 3, 5, 6, 7, 8, 9} and B = {2, 3, 6, 9, 10}.