# Negations

### Negations

#### Lessons

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.
• Introduction
Negations Overview:
a)
Definition of Negations and Examples

• 1.
Negation of the Statement

Write the negation of each statement:

a)
The sun rises from the east.

b)
$1+1=0$

c)
January is the first month of the year.

d)
The Eiffel Tower is in Japan.

e)
A square has 7 sides.

• 2.
Truth Value of a Negation

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

a)
A snake is a reptile.

b)
The measure of an acute angle is greater than 90°.

c)
$5+5+5=555$

d)
$\frac{5}{6}$ 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) ~$r$

• 4.
Double Negation

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

a)
A quarter of an hour is 15 minutes

b)
There is caffeine in coffee.

c)
The ocean has salt water.