Browse the Topics, Table of Contents, and Index
Follow us:
Twitter Facebook

3.1 Sets & Set Diagrams

3.1 Sets & Set Diagrams
  • 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.
  • Consumer Suggestion

    Have you thought about getting a pet? If you'd like to adopt a pet, you can search by location and type on Adopt-a-pet or visit your local humane society.

    For ten tips on how to help animals in your community, visit the American Society for the Prevention of Cruelty to Animals (ASPCA).

  • 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.

  • Comments (1)

    These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
    When posting a comment, you agree to our Terms of Use.

                 ___     _    _     _____     ______  
        ___     / _ \\  | |  | ||  |  ___||  /_   _// 
       /   ||  / //\ \\ | |/\| ||  | ||__      | ||   
      | [] || |  ___  |||  /\  ||  | ||__     _| ||   
       \__ || |_||  |_|||_// \_||  |_____||  /__//    
        -|_|| `-`   `-` `-`   `-`  `-----`   `--`     
    Showing 1 comments
    Subscribe by RSS
    system user
    Ron Larson (author)1 decade ago |
    Some people find that set diagrams help them to visually see relationships. I am one of those people. If you are too, then you will enjoy this section.