Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Let the universal set : U = { 1 , 2 , 3 , . . . , 10 } .Let A = { 1 , 4 , 7 , 10 }, B = { 1 , 2 , 3 , 4 , 5 }, and C = { 2 , 4 , 6 , 8 }. ?

Let the universal set : U = { 1 , 2 , 3 , . . . , 10 } .Let A = { 1 , 4 , 7 , 10 }, B = { 1 , 2 , 3 , 4 , 5 }, and C = { 2 , 4 , 6 , 8 }. List the elements of each set.

1. U ′

2. B ∩ ∅

3/ B ∩ U

4. B ′ ∩ ( C − A )

5. A'∩ B' U C

1 Answer

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  • 2 months ago
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    1.

    U'

    = U - U

    = ∅

    2.

    B ⋂ ∅

    = B

    = {1, 2, 3, 4, 5}

    3.

    B ⋂ U

    = B

    = {1, 2, 3, 4, 5}

    4.

    B' ⋂ (C - A)

    = (U - B) ⋂ (C - A)

    = ({1, 2, 3, ……, 10} - {1, 2, 3, 4, 5}) ⋂ ({2, 4, 6, 8} - {1, 4, 7, 10})

    = {6, 7, 8, 9, 10} ⋂ {2, 6, 8}

    = {6, 8}

    5.

    A' ⋂ B' ⋃ C

    = (U - A) ⋂ {U - B} ⋃ C

    = ({1, 2, 3, ……, 10} - {1, 4, 7, 10}) ⋂ ({1, 2, 3, ……, 10} - {1, 2, 3, 4, 5}) ⋃ {2, 4, 6, 8}

    = {1, 2, 3, 5, 6, 8, 9} ⋂ {6, 7, 8, 9, 10} ⋃ {2, 4, 6, 8}

    = {6, 8, 9} ⋃ {2, 4, 6, 8}

    = {2, 4, 6, 8, 9}

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