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18 December, 17:44

A subset of clients is described that the consultant could find using her database. HINT [See Example 4.] The clients who either do not owe her money, have done at least $10,000 worth of business with her, or have employed her in the last year. Write the subset in terms of A, B, and C. A ∪ B ∪ C A ∪ B' ∪ C' A' ∪ B ∪ C A' ∪ B' ∪ C' A' ∪ B ∪ C'

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  1. 18 December, 18:06
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    Write the subset in terms of A, B, and C.

    1. A ∪ B ∪ C

    2. A ∪ B' ∪ C'

    3. A' ∪ B ∪ C

    4. A' ∪ B' ∪ C'

    5. A' ∪ B ∪ C'

    Answer:

    1. A ∪ B ∪ C = {Acme, Brothers, Crafts, Dion, Effigy, Global, Hilbert}

    2. A ∪ B' ∪ C' = {Acme, Brothers, Craft, Dion, Effigy, Floyd, Global, Hilbert}

    3. A' ∪ B ∪ C = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global}

    4. A' ∪ B' ∪ C' = {Brothers, Dion, Effigy, Floyd, Gilbert, Hilbert}

    5. A' ∪ B ∪ C' = {Acme, Brothers, Crafts, Dion, Floyd, Hilbert}

    Step-by-step explanation:

    Given

    From the hint in the question above

    A = Set of all clients who do not owe her money.

    A = {Acme, Craft, Dion, Effigy, Global, Hilbert}

    B = Set of all clients that have done at least $10,000 worth of business with her

    B = {Acme, Brothers, Crafts, Dion}

    C = Set of all clients who have employed her in the last year

    C = {Acme, Crafts, Effigy, Global}

    Let U = The Universal Set = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert}

    1. A ∪ B ∪ C:

    This means the set of every elements present in A, B and C without repetition of any element of the set

    Given that

    A = {Acme, Craft, Dion, Effigy, Global, Hilbert}

    B = {Acme, Brothers, Crafts, Dion}

    C = {Acme, Crafts, Effigy, Global}

    A ∪ B ∪ C = {Acme, Brothers, Crafts, Dion, Effigy, Global, Hilbert}

    2. A ∪ B' ∪ C'

    Given that

    A = {Acme, Craft, Dion, Effigy, Global, Hilbert}

    B' = Sets of all elements in the universal set but not in B

    So, B' = {Effigy, Floyd, Global, Hilbert}

    C' = Sets of all elements in the universal set but not in C

    So, C' = {Brothers, Dion, Floyd, Hilbert}

    A ∪ B' ∪ C' = {Acme, Brothers, Craft, Dion, Effigy, Floyd, Global, Hilbert}

    3. A' ∪ B ∪ C

    A' = Sets of all elements in the universal set but not in A

    So, A' = {Brothers, Floyd}

    B = {Acme, Brothers, Crafts, Dion}

    C = {Acme, Crafts, Effigy, Global}

    A' ∪ B ∪ C = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global}

    4. A' ∪ B' ∪ C'

    A' = Sets of all elements in the universal set but not in A

    So, A' = {Brothers, Floyd}

    B' = Sets of all elements in the universal set but not in B

    So, B' = {Effigy, Floyd, Global, Hilbert}

    C' = Sets of all elements in the universal set but not in C

    So, C' = {Brothers, Dion, Floyd, Hilbert}

    A' ∪ B' ∪ C' = {Brothers, Dion, Effigy, Floyd, Gilbert, Hilbert}

    5. A' ∪ B ∪ C'

    A' = Sets of all elements in the universal set but not in A

    So, A' = {Brothers, Floyd}

    B = {Acme, Brothers, Crafts, Dion}

    C' = Sets of all elements in the universal set but not in C

    So, C' = {Brothers, Dion, Floyd, Hilbert}

    A' ∪ B ∪ C' = {Acme, Brothers, Crafts, Dion, Floyd, Hilbert}
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