Find the sets a and b if a - b = {1, 5, 7, 8}, b - a = {2, 10}, and a ∩ b = {3, 6, 9}.

Solution :

Given that the difference of sets a and b:

• a - b = {1, 5, 7, 8}
• b - a = {2, 10}, and
• intersection of sets is: a ∩ b = {3, 6, 9}

Using the sets formula, we know that a = (a - b) U (a ⋂ b)

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

= {1, 3, 5, 6, 7, 8, 9} (to understand how to find the union of two sets, click here)

b = (b - a) U (a ⋂ b)

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

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

Therefore, the value of sets a and b are {1, 3, 5, 6, 7, 8, 9} and {2, 3, 6, 9, 10}.

Find the sets a and b if a - b = {1, 5, 7, 8}, b - a = {2, 10}, and a ∩ b = {3, 6, 9}.

Summary :

If a - b = {1, 5, 7, 8}, b - a = {2, 10}, and a ∩ b = {3, 6, 9} then the sets a and b are {1, 3, 5, 6, 7, 8, 9} and {2, 3, 6, 9, 10} respectively.