# Hero Definition Essay Negation Geometry

## Presentation on theme: "DEFINITION ESSAY You can use these strategies of definition to write a well organized and supported essay."— Presentation transcript:

1 DEFINITION ESSAYYou can use these strategies of definition to write a well organized and supported essay.

2 FUNCTIONThis strategy helps the reader understand how the concept (idea) functions or operates in the real world. It may be what the idea does or it’s intended use. It is usually the action or “verb” aspect of the idea.

3 FUNCTION STRATEGYCARTRANSPORATIONFAST TRAVELSHELTERA/C

4 **FUNCTION STRATEGY FRIEND PROVIDES COMPANIONSHIP IS CARING AND KIND**

MAKES YOU HAPPYPROVIDES ADVICE OR GUIDANCE

5 EXAMPLE STRATEGYThis strategy helps the reader understand your definition by providing concrete examples from fiction or non–fiction. Often times support can come from text.

6 EXAMPLE STRATEGYCARHONDABMWCHEVROLETCADILLAC

7 **EXAMPLE STRATEGY FRIEND Max and Freak from Freak the Mighty**

Spongebob and Sandy- from the cartoonWinnie the Pooh and PigletMy friend Kathy and me

8 NEGATION STRATEGYThis strategy clarifies what the idea or concept IS by showing what is it NOT.

9 NEGATION STRATEGYCARBICYCLEAIRPLANEBOATMOTORCYCLELAWN MOVER

10 **NEGATION STRATEGY FRIEND LIAR BULLY**

SOMEONE WHO INTENTIONALLY HURTS YOUSOMEONE WHO CANNOT BE T RUSTEDSOMEONE WHO MAKES FUN OF YOU

11 NOW IT’S YOUR TURNUSING THE 3 STRATEGIES OF FUNCTION , EXAMPLE AND NEGATION ,WRITE A FULL RESPONSE TO ANSWER THE QUESTION,“WHAT IS A HERO?”

12 **How to organize your essay**

1st paragraph: Intro with thesis statement. Thesis statement answers the question:What defines a hero (to me)Thesis statement: The controlling idea of your essay.Include the 3 points you will make in your essay.

13 **2nd paragraph: Use the Function strategy of defining**

3rd paragraph: Use the Example strategy4th paragraph: Use the Negation strategy5th paragraph: Conclusion

14 Label the paragraphs:F for FunctionE for ExampleN for Negation

15 Typed12 point fontDouble spaceTimes new roman, arial, calibri

## Logic and Mathematical Statements

## Worked Examples

## Negation

Sometimes in mathematics it's important to determine what the opposite of a given mathematical statement is. This is usually referred to as "negating" a statement. One thing to keep in mind is that if a statement is true, then its negation is false (and if a statement is false, then its negation is true).Let's take a look at some of the most common negations.

### Negation of "A **or** B".

Before giving the answer, let's try to do this for an example. Consider the statement "You are either rich or happy." For this statement to be false, you can't be rich

*and*you can't been happy. In other words, the opposite is to be not rich

*and*not happy. Or if we rewrite it in terms of the original statement we get "You are not rich and not happy."

If we let A be the statement "You are rich" and B be the statement "You are happy", then the negation of "A or B" becomes "Not A and Not B."

In general, we have the same statement: The negation of "A or B" is the statement "Not A

**Not B."**

*and*### Negation of "A **and** B".

Again, let's analyze an example first. Consider the statement "I am both rich and happy." For this statement to be false I could be

*either*not rich

*or*not happy. If we let A be the statement "I am rich" and B be the statement "I am happy", then the negation of "A and B" becomes "I am not rich

*or*I am not happy" or "Not A or Not B".

### Negation of "**If** A, **then** B".

To negate a statement of the form "If A, then B" we should replace it with the statement "**A and Not B**". This might seem confusing at first, so let's take a look at a simple example to help understand why this is the right thing to do.

Consider the statement "If I am rich, then I am happy." For this statement to be false, I would need to be rich and not happy. If A is the statement "I am rich" and B is the statement "I am happy,", then the negation of "A $\Rightarrow$ B" is "I am rich" = A, and "I am not happy" = not B.

So the negation of "

**if**A,

**then**B" becomes "A

**and not**B".

### Example.

Now let's consider a statement involving some mathematics. Take the statement "If n is even, then $\frac{n}{2}$ is an integer." For this statement to be false, we would need to find an even integer $n$ for which $\frac{n}{2}$ was not an integer. So the opposite of this statement is the statement that "$n$ is even and $\frac{n}{2}$ is not an integer."### Negation of "For every ...", "For all ...", "There exists ..."

Sometimes we encounter phrases such as "for every," "for any," "for all" and "there exists" in mathematical statements.### Example.

Consider the statement "For all integers $n$, either $n$ is even or $n$ is odd". Although the phrasing is a bit different, this is a statement of the form "If A, then B." We can reword this sentence as follows: "If $n$ is any integer, then either $n$ is even or $n$ is odd."How would we negate this statement? For this statement to be false, all we would need is to find a single integer which is not even and not odd. In other words, the negation is the statement "There exists an integer $n$, so that $n$ is not even and $n$ is not odd."

In general, when negating a statement involving "for all," "for every", the phrase "for all" gets replaced with "there exists." Similarly, when negating a statement involving "there exists", the phrase "there exists" gets replaced with "for every" or "for all."

### Example. Negate the statement "If all rich people are happy, then all poor people are sad."

First, this statement has the form "If A, then B", where A is the statement "All rich people are happy" and B is the statement "All poor people are sad." So the negation has the form "A and not B." So we will need to negate B. The negation of the statement B is "There exists a poor person who is not sad."Putting this together gives: "All rich people are happy, but there exists a poor person who is not sad" as the negation of "If all rich people are happy, then all poor people are sad."

**Summary.**

Statement | Negation |

"A or B" | "not A and not B" |

"A and B" | "not A or not B" |

"if A, then B" | "A and not B" |

"For all x, A(x)" | "There exist x such that not A(x)" |

"There exists x such that A(x)" | "For every x, not A(x)" |

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