### 3.1 Sets & Set Diagrams

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• Math Help

In the set diagram on page 107, the fish class is drawn as the complement of the union of birds, amphibians, mammals, and vertebrates.

• Consumer Suggestion

Using the latest in high definition filming techniques, the Discovery Channel spent four years making "Life," a series chronicling the ways animals across the world fight for survival. To watch video clips and see behind-the-scenes shots, visit Discovery Channel's "Life."

• Checkpoint Solution

Here is one possible set diagram for this information.

Note that for the purpose of illustration, we have classified fish (like sharks) that have cartilage skeletons as vertebrate. Sharks and other cartilaginous fish (skates and rays) have skeletons made of cartilage and connective tissue. Cartilage has about half the density of bone. This reduces the skeleton's weight, saving energy.

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```  ____     __   __     _____    _____    _    _
|  _ \\   \ \\/ //   / ___//  |  ___|| | \  / ||
| |_| ||   \ ` //    \___ \\  | ||__   |  \/  ||
| .  //     | ||     /    //  | ||__   | .  . ||
|_|\_\\     |_||    /____//   |_____|| |_|\/|_||
`-` --`     `-`'   `-----`    `-----`  `-`  `-`

```
Guest   9 years ago |
I'm not sure I understand your cousin's concern with the checkpoint on Math & You page 107. I'm looking at a biology text that says, "The first vertebrates to possess both jaws and paired fins were the cartilaginous fishes, so called because their skeletons were made of firm but resilient cartilage." This includes sharks. Sharks are also listed as vertebrates at every web site I visit (encylcopedia.com, wikepedia, numerous educational sites). This site breaks it down nicely: http://users.tamuk.edu/kfjab02/Biology/Vertebrate%20Zoology/b3405_ch01.htm
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Ron Larson (author)9 years ago |
When my cousin Michael read the checkpoint question, he wrote and told me that I might get some criticism from a biologist because sharks do not have regular skeletons of bone, as do other vertebrates. If you agree with this criticism, please drop me a note and suggest a way of making the checkpoint question more biologically correct.
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Ron Larson (author)9 years ago |
Thanks for leaving the comment! Yes, I like pictures too. When my son was little, we bought him a colorful book about mathematics. I remember thinking how different it was to see a "math book" that was actually colorful and visually stimulating.
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Guest   9 years ago |
There are a lot of pictures in this book. It's different than what I'm used to for textbooks, but I like it.
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