If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {0, 2, 4, 6, 8}, B = {1, 3, 5, 7, 9}, C = {2, 3, 4, 5}, and D = {1, 6, 7}, list th

Question

If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A =
{0, 2, 4, 6, 8}, B = {1, 3, 5, 7, 9}, C = {2, 3, 4, 5}, and
D = {1, 6, 7}, list the elements of the sets corresponding
to the following events:
a) A∪C
b) A∩B
c) C′
d) (C′∩D)∪B
e) (S∩C)′
f) A∩C∩D′

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Piper 2 weeks 2021-09-10T19:15:13+00:00 1 Answer 0

Answers ( )

    0
    2021-09-10T19:16:37+00:00

    Answer:

    a) = {0, 2, 3, 4, 5, 6, 8}, b = {0} empty set. c =  {0, 1, 6, 7, 8, 9} d =  {0, 1, 3, 5, 6, 7, 8, 9} e =  {0, 1, 5, 6, 7, 8, 9} f = {2,4} .

    Step-by-step explanation:

    Given:

    S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

    A =  {0, 2, 4, 6, 8}

    B = {1, 3, 5, 7, 9}

    C = {2, 3, 4, 5}

    D = {1, 6, 7}

    Solution:

    a) A∪C = A + C – A∩C

                = {0, 2, 4, 6, 8} + {2, 3, 4, 5} – {2, 4}

                = {0, 2, 2, 3, 4, 4, 5, 6, 8} –  {2, 4}

                = {0, 2, 3, 4, 5, 6, 8}

    b)  A∩B = ?

    A∪B = A + B –   A∩B

    A∪B +  A∩B = A + B

    A∩B =  A + B – A∪B

            =   {0, 2, 4, 6, 8} +  {1, 3, 5, 7, 9} –   {0, 1, 2, 3, 4, 5, 6, 8, 9}

            = {0,1, 2, 3, 4, 5, 6,7, 8, 9} – {0, 1, 2, 3, 4, 5, 6, 8, 9}

    A∩B = {0} empty set.

    c) C′ = S – C

           = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} –  {2, 3, 4, 5}

           = {0, 1, 6, 7, 8, 9}

    d) (C′∩D)∪B = ?

    (C′∩D) = {0, 1, 6, 7, 8, 9} ∩ {1, 6, 7}

               = {1, 6, 7}

    B =  {1, 3, 5, 7, 9}

    (C′∩D)∪B = (C′∩D) + B – (C′∩D)∩B

                    = {0, 1, 6, 7, 8, 9} +  {1, 3, 5, 7, 9} –  {1, 7, 9,}

                    = {0, 1, 1, 3, 5, 6, 7, 7, 8, 9, 9} –  {1, 7, 9,}

                    = {0, 1, 3, 5, 6, 7, 8, 9}

    e) (S∩C)′ = S – (S∩C)′

    (S∩C) =  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ∩ {2, 3, 4, 5}

                  = {2, 3, 4, 5}

    (S∩C)′ = S –  (S∩C)

               =  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} –  {2, 3, 4, 5}

               =   {0, 1, 5, 6, 7, 8, 9}

    f) A∩C∩D′ = ?

    D′ = S – D

       = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 6, 7}

       = {0, 2, 3, 4, 5, 8, 9}

    A∩C∩D′ = {0, 2, 4, 6, 8} ∩  {2, 3, 4, 5} ∩ {0, 2, 3, 4, 5, 8, 9}

                  =  {2,4}

           

           

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