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

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

A ∪ B: Elements that are contained in A or B

A ∩ B: Elements that are contained in A and B

A - B: Elements that are contained in A but not contained in B

## Answer: A = {1, 3, 5, 6, 7, 8, 9} and B = {2, 3, 6, 9, 10}

We will use the above definitions to find the sets A and B.

## Explanation:

A = (A ∩ B) ∪ (A - B)

= {3, 6, 9} ∪ {1, 5, 7, 8}

= {1, 3, 5, 6, 7, 8, 9}

B = (A ∩ B) ∪ (B - A)

= {3, 6, 9} ∪ {2, 10}

= {2, 3, 6, 9, 10}

### Therefore, A = {1, 3, 5, 6, 7, 8, 9} and B = {2, 3, 6, 9, 10}

Learn from the best math teachers and top your exams

- Live one on one classroom and doubt clearing
- Practice worksheets in and after class for conceptual clarity
- Personalized curriculum to keep up with school