1. Databases A freelance computer consultant keeps a database of her clients, which contains the names

S = {Aces, Brothers, Cores, Dion, Energy, Floyd, Global, Hilbert}.

These clients owe her money:

A = {Aces, Cores, Energy, Global}.

These clients have done at least $40,000 worth of business with her:

B = {Aces, Brothers, Cores, Dion}.

These clients have employed her in the last year:

C = {Aces, Cores, Dion, Energy, Global, Hilbert}.

A subset of clients is described that the consultant could find using her database.

The clients who do not owe her money or have employed her in the last year.

Write the subset in terms of A, B, and C.

A BA B A CA CA C

List the clients in that subset.

{Aces, Cores}{Floyd, Brothers} {Aces, Energy, Cores, Global, Brothers, Dion, Floyd, Hilbert}{Aces, Energy, Cores, Global}

2.

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If

n(A) = 105, n(A B) = 158, and n(A B) = 46, find n(B).

3.

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For the given decision algorithm, find how many outcomes are possible.

Alternative 1

• Step 1: 1 outcome
• Step 2: 4 outcomes

Alternative 2

• Step 1: 5 outcomes
• Step 2: 4 outcomes
• Step 3: 1 outcome

outcomes

4.

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A ternary digit is either 0, 1, or 2. How many sequences of ten ternary digits are possible containing a single 0 and a single 1?

outcomes

5.

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Let A = {small, medium, large}, B = {white, magenta}, and C = {triangle, square}. HINT [See Example 5.] Represent A C as cells in a spreadsheet.

	triangle	square
small	---Select--- small medium large ---Select--- triangle square white magenta	---Select--- small medium large ---Select--- triangle square white magenta
medium	---Select--- small medium large ---Select--- triangle square white magenta	---Select--- small medium large ---Select--- triangle square white magenta
large	---Select--- small medium large ---Select--- triangle square white magenta	---Select--- small medium large ---Select--- triangle square white magenta