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13 August, 11:01

Let A = {1, 3, 6, 8, 9} B = {2, 5, 6, 7, 8} C = {1, 4, 6, 7, 8, 9} and D = {1,2}

Calculate (A∪B) ∩C

Calculate P (D), i. e., power set

Is (A ∩ B) ⊆C? Why or why not?

What is (B ∩ C) * {1,2}?

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  1. 13 August, 11:59
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    Answer with Step-by-step explanation:

    Let A = {1, 3, 6, 8, 9}

    B = {2, 5, 6, 7, 8}

    C = {1, 4, 6, 7, 8, 9}

    and D = {1,2}

    Calculate (A∪B) ∩C

    A∪B={1,2,3,5,6,7,8,9} (union of two sets is the set of element which are in any one of the two sets or in both)

    (A∪B) ∩C = {1,6,7,8,9} (intersection of two sets are the set of elements which are in both the sets)

    Calculate P (D), i. e. power set of D

    P (D) = {Ф,{1},{2},{1,2}} (Power set of any set is the collection of all the subsets of that set)

    Is (A ∩ B) ⊆C? Why or why not?

    A∩B={6,8}⊆{1, 4, 6, 7, 8, 9} = C

    Hence, (A ∩ B) ⊆C

    What is (B ∩ C) * {1,2}?

    B∩C={6,7,8}

    (B ∩ C) * {1,2}={6,7,8} * {1,2}

    ={ (6,1), (6,2), (7,1), (7,2), (8,1), (8,2) }
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