Question

Arrange the given steps in the correct order to find A and B if A and B are two sets where A – B = {1, 5, 7, 8}, B – A = {2, 10} and A ∩ B = {3, 6, 9}.

Answer 1

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

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

Explanation:

Here as given in the question:

A – B = {1, 5, 7, 8} ⇒ {1, 5, 7, 8} is in A not in B.

B – A = {2, 10} ⇒ {2, 10} is in B not in A

A ∩ B = {3, 6, 9} ⇒ {3, 6, 9} is BOTH in A and B.

Step 1:

Set A can also be expressed as : A = (A - B) ∪ (A ∩ B)

Set A can also be expressed as : B = (B - A) ∪ (A ∩ B)

Step 2:

Substituting the values of (A - B) and (B - A)

A = {1, 5, 7, 8} ∪ {3, 6, 9}

B = {2, 10} ∪ {3, 6, 9}.

Step 3:

Finding the UNION of the above two sets, we get:

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

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