# Negations

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##### Intros
###### Lessons
1. Negations Overview:
Definition of Negations and Examples
##### Examples
###### Lessons
1. Negation of the Statement

Write the negation of each statement:

1. The sun rises from the east.
2. $1+1=0$
3. January is the first month of the year.
4. The Eiffel Tower is in Japan.
5. A square has 7 sides.
2. Truth Value of a Negation

Write the negation of each statement, and determine the truth value:

1. A snake is a reptile.
2. The measure of an acute angle is greater than 90°.
3. $5+5+5=555$
4. $\frac{5}{6}$ is a fraction.
3. The symbols represent the following statements

$p$: A pentagon has 5 sides
$q$: United States is a city
$r$: Chairs have four legs

Write a complete sentence in words to show what the symbols means, and find the truth value:

i) ~$p$
ii) ~$q$
iii) ~$r$
1. Double Negation

Determine the truth value of the statement. Negate it twice, write it in a complete sentence, and determine the new truth value:

1. A quarter of an hour is 15 minutes
2. There is caffeine in coffee.
3. The ocean has salt water.
###### Topic Notes
The negation of a statement is the opposite of a statement. We denote it with either "not" or the symbol ~. The negation gives the opposite of the truth value. For example,
$p$: A square is a rectangle
~ $p$: A square is not a rectangle $p$ is true, so ~$p$ is false.