### 3.1 Sets & Set Diagrams

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• Math Help

In mathematics, formal set diagrams are called Venn diagrams or Euler diagrams. In this text, we are not using these formal types of set diagrams. The diagrams we are using are informal and are intended only to help understand relationships between sets or statements.

If the set diagram on page 102 were a formal Venn diagram, it would have 4 regions.

1. In A but not in B.
2. In both A and B.
3. In B but not in A.
4. Not in A or B.

The outer rectangle in this diagram is called the universal set. It contains all the objects that are being considered. For instance, in Example 1, the universal set could be the set of all households in the United States.

1. Own a bird but not a cat.
2. Own both a bird and a cat.
3. Own a cat but not a bird.
4. Don't own a cat or a bird.
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• Checkpoint Solution

Throughout this chapter, please don't allow yourself to get caught up in the formality of set diagrams. The purpose of including them in this book is to help you analyze statements. Moreover, when we list an answer to a question that asks for a set diagram, remember that the diagram we are showing is only one of several that could be drawn.

For this question, it helps to start by summarizing the given information

• 120 million women in the United States
• 5.7 million of these rode a motorcycle in the past year
• 25 million Americans rode motorcycles in the past year

Here is one way to draw this information.

Here is another way to draw the same information.

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```             ___     _    _     _____     ______
___     / _ \\  | |  | ||  |  ___||  /_   _//
/   ||  / //\ \\ | |/\| ||  | ||__      | ||
| [] || |  ___  |||  /\  ||  | ||__     _| ||
\__ || |_||  |_|||_// \_||  |_____||  /__//
-|_|| `-`   `-` `-`   `-`  `-----`   `--`
`-`
```