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}