### 3.4 Fallacies in Logic

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• 9. Bluffing at Cards

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

When Jack is bluffing, he sets a chip on his cards. Jack set a chip on his cards, so I know he's bluffing.

• Worked-Out Solution

Here is one possible invalid syllogism.

 • Premise: If Jack is bluffing, then he sets a chip on his cards. • Premise: Jack set a chip on his cards. • Conclusion: Therefore, Jack is bluffing.

This type of fallacy is called affirming the consequent.

 • Premise: If P, then Q. • Premise: Q. • Conclusion: Therefore, P.

In the first premise, Q is called the consequent. The name affirming the consequent comes from the fact that the second premise states that Q is true.

Here is one way to draw a diagram to analyze this fallacy.

Stating that a syllogism is a fallacy simply means that the conclusion was not obtained by logical deduction. It does not mean that the conclusion of the syllogism is false.

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```  ____       ___               __   __   __   __
|  _ \\    / _ \\    ____     \ \\/ //  \ \\/ //
| |_| ||  | / \ ||  |    \\    \ ` //    \   //
| .  //   | \_/ ||  | [] ||     | ||     / . \\
|_|\_\\    \___//   |  __//     |_||    /_//\_\\
`-` --`    `---`    |_|`-`      `-`'    `-`  --`
`-`
```
• 10. Friendly Behavior

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

When Rich wants a favor, he starts acting really friendly. Rich has been acting really friendly today, so I know he wants something.

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

```
• 11. Family Traits

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

Greg's friend Dylan is very conservative. Greg concludes that everyone in Dylan's family must be very conservative.

• Worked-Out Solution

Here is one way to draw a diagram to analyze the conclusion.

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

```
• 12. Power Outage

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

Erica awakens at midnight and discovers the power is out at her house. She looks out her window and sees that all of her neighbors' windows are dark. She concludes that they must have lost their power too.

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

```

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

Kyle is buying a dress for his wife. He knows she doesn't like the color blue. So, he picks out a yellow dress and concludes that she will like it because it isn't blue.

• Worked-Out Solution

Here is one way to draw a diagram to analyze the conclusion.

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

```
• 14. Approval of Tattoos

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

Kimberly's mother doesn't approve of boys with tattoos. Kimberly's new boyfriend doesn't have any tattoos, so she concludes that her mother will approve of him.

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

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

Tom is ordering pizza for his friends. He recalls that his friend David doesn't like pepperoni. So, he orders a pizza with mushrooms and concludes that David will eat it because it doesn't have pepperoni on it.

• Worked-Out Solution

Here is one way to draw a diagram to analyze the conclusion.

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```  _  _     ______    _____    __   __  __    __
| \| ||  /_   _//  |__  //   \ \\/ // \ \\ / //
|  ' ||   -| ||-     / //     \ ` //   \ \/ //
| .  ||   _| ||_    / //__     | ||     \  //
|_|\_||  /_____//  /_____||    |_||      \//
`-` -`   `-----`   `-----`     `-`'       `

```
• 16. Feeling Sick

Draw a set diagram to analyze the conclusion. (See Example 3 and Example 4.)

I am feeling sick this morning. It must be because of the sushi I ate last night. Everyone who ate the sushi must be sick by now.

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```   _____    _____     ______    _____     ______