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29 January, 23:09

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}.

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  1. 30 January, 01:23
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    A = {1, 3, 5, 6, 7, 8, 9}

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

    Step-by-step 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}
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