Question

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

Answer 1

The sets A and B are determined based on the given information: A - B = {1, 5, 7, 8}, B - A = {2, 10}, and A ∩ B = {3, 6, 9}. A = {1, 5, 7, 8, 3, 6, 9} and B = {2, 10, 3, 6, 9}.

Step-by-step explanation:

The sets A and B can be determined by examining the given information:

1. A - B = {1, 5, 7, 8}
2. B - A = {2, 10}
3. A ∩ B = {3, 6, 9}

From the above information, we can conclude that:

• The elements of A that are not in B are {1, 5, 7, 8}.
• The elements of B that are not in A are {2, 10}.
• A and B share the common elements {3, 6, 9}.

Therefore, the sets A and B can be defined as:

• A = {1, 5, 7, 8, 3, 6, 9}
• B = {2, 10, 3, 6, 9}