### 3.3 Deductive & Inductive Reasoning

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• 17. Dinosaurs

Use the locations of the fossil findings to infer where each type of dinosaur lived. Outline your inductive reasoning and draw a set diagram for each type of dinosaur. (See Example 5 and Example 6.)

• Worked-Out Solution

In each case, you can use inductive reasoning to infer that each type of dinosaur lived only in the regions where its fossils have been found.

Troodon: Conclusion based on pattern

• The only places that Troodon fossils have been found are Wyoming, Montana, Alberta, and Alaska.
• Therefore, the only places that Troodon lived were Wyoming, Montana, Alberta, and Alaska.

Notice that this conclusion is illogical. Based on logic, you should probably revise the statement to conclude that Troodon also lived in British Columbia and in Northwest Territory.

Velociraptor: Conclusion based on pattern

• The only places that Velociraptor fossils have been found are China and Mongolia.
• Therefore, the only places that Velociraptor lived were China and Mongolia.

Giganotosaurus: Conclusion based on pattern

• The only places that Giganotosaurus fossils have been found is Argentina.
• Therefore, the only places that Giganotosaurus lived was Argentina.

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```  ______     ___      ______    ______   ______
/_____//   / _ \\   /_____//  /_   _// |      \\
`____ `   / //\ \\  `____ `    -| ||-  |  --  //
/___//   |  ___  || /___//     _| ||_  |  --  \\
`__ `    |_||  |_|| `__ `     /_____// |______//
/_//     `-`   `-`  /_//      `-----`  `------`
`-`                 `-`
```
Cody (moderator)1 decade ago |
Like most kids, I was a big dinosaur fan when I was younger. One of my favorite tv shows was "Dinosaurs." I recently learned that you can buy dvd's of the whole series. However, sometimes shows you watched as a kid don't seem so good when you watch them as an adult. Anyone recommend the dvd's, or should I pass?
2
• 18. Velociraptor

Does the absence of Velociraptor fossils in North America prove that Velociraptor did not live there? Explain your reasoning. (See Example 5 and Example 6.)

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

```
There are no comments.
• 19. Giganotosaurus

Giganotosaurus fossils have been dated to about 100 to 95 million years ago. What can you infer about the time period in which all Giganotosaurus lived? Outline your inductive reasoning and draw a set diagram. (See Example 5 and Example 6.)

• Worked-Out Solution

Because all Giganotosaurus fossils that have been found date to a period from 100 million to 95 million years ago, you can infer that this was the only time period in which this type of dinosaur lived. Remember that 5 million years is an incredibly long period of time.

Giganotosaurus: Conclusion based on pattern

• All Giganotosaurus fossils have been dated to about 100 to 95 million years ago.
• Therefore all Giganotosaurus lived about 100 to 95 million years ago.

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``` ______    _    _    _    _     _____     _____
|      \\ | || | || | |  | ||  |  ___||  |__  //
|  --  // | || | || | |/\| ||  | ||__      / //
|  --  \\ | \\_/ || |  /\  ||  | ||__     / //__
|______//  \____//  |_// \_||  |_____||  /_____||
`------`    `---`   `-`   `-`  `-----`   `-----`

```
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• 20. Troodon

Troodon fossils have been dated to about 75 to 65 million years ago. What can you infer about the time period in which all Troodon lived? Outline your inductive reasoning and draw a set diagram. (See Example 5 and Example 6.)

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```  _____    __   __   _    _      ___
/  ___||  \ \\/ // | || | ||   / _ \\    ____
| // __     \ ` //  | || | ||  / //\ \\  |    \\
| \\_\ ||    | ||   | \\_/ || |  ___  || | [] ||
\____//     |_||    \____//  |_||  |_|| |  __//
`---`      `-`'     `---`   `-`   `-`  |_|`-`
`-`
```
Guest   4 years ago |
wth is this nothing to do with math smh
0
• 21. Velociraptor

Velociraptor fossils have been dated to about 75 to 71 million years ago. Is it likely that Velociraptor encountered Troodon or Giganotosaurus? Explain your reasoning. (See Example 5 and Example 6.)

• Worked-Out Solution

Use the information from the map and the information given in Exercises 19, 20, and 21. You can organize the information in a table.

From the current fossil record it is extremely unlikely that Velociraptor encountered Gigantosaurus. The two species appear to have lived millions of years apart.

Although the era in which Velociraptor lived overlapped with the era in which Troodon lived, it appears that they lived in different parts of the world, several thousand miles from each other. So, it is unlikely that the two species ever encountered each other.

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```__    __   _    _     ______     ___
\ \\ / // | || | ||  /_____//   / _ \\    ____
\ \/ //  | || | ||  `____ `   / //\ \\  |    \\
\  //   | \\_/ ||  /___//   |  ___  || | [] ||
\//     \____//   `__ `    |_||  |_|| |  __//
`       `---`    /_//     `-`   `-`  |_|`-`
`-`                 `-`
```
There are no comments.
• 22. Tyrannosaurus Rex

Research the locations in which Tyrannosaurus rex fossils have been found and the time period in which Tyrannosaurus rex lived. Is it likely that Tyrannosaurus rex encountered Troodon, Velociraptor, or Giganotosaurus? Explain your reasoning. (See Example 5 and Example 6.)

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When posting a comment, you agree to our Terms of Use.

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

```