Question

A freelance computer consultant keeps a database of her clients, which contains the names S = {Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert}. The following clients owe her money: A = {Acme, Crafts, Effigy, Global}. The following clients have done at least $10,000 worth of business with her: B = {Acme, Brothers, Crafts, Dion}. The following clients have employed her in the last year: C = {Acme, Crafts, Dion, Effigy, Global, Hilbert}.

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'

List the clients in the subset.

{Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert}

{Acme, Brothers, Crafts, Dion}

{Acme, Crafts, Dion, Effigy, Global, Hilbert}

{Acme, Crafts, Effigy, Global}

∅

Answer 1

The clients who either do not owe her money

A'=  {Brothers, Dion, Floyd, Hilbert}

Clients have done at least $10,000 worth of business with her:

B = {Acme, Brothers, Crafts, Dion}

Clents have employed her in the last year:

C = {Acme, Crafts, Dion, Effigy, Global, Hilbert}.

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.

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