Negations - Logic

Negations

Lessons

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.

- a)
  Definition of Negations and Examples
1.
Negation of the Statement
Write the negation of each statement:
2.
Truth Value of a Negation
Write the negation of each statement, and determine the truth value:
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:

Negations

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Intro Lesson

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Lesson: 1a

Lesson: 1b

Lesson: 1c

Lesson: 1d

Lesson: 1e

Lesson: 2a

Lesson: 2b

Lesson: 2c

Lesson: 2d

Lesson: 3

Lesson: 4a

Lesson: 4b

Lesson: 4c

Intro

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Lessons

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, ppp: A square is a rectangle ~ ppp: A square is not a rectangle ppp is true, so ~ppp is false.

Intro Lesson

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 1+1=0 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 5+5+5=555 5+5+5=555

d)

56\frac{5}{6}65​ is a fraction.

3.

The symbols represent the following statements ppp: A pentagon has 5 sides qqq: United States is a city rrr: Chairs have four legs Write a complete sentence in words to show what the symbols means, and find the truth value: i) ~ppp ii) ~qqq iii) ~rrr

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.

Negations

Don't just watch, practice makes perfect.

We have over 160 practice questions in Geometry for you to master.

or

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.

Negation of the Statement
Write the negation of each statement:

$1+1=0$

Truth Value of a Negation
Write the negation of each statement, and determine the truth value:

$5+5+5=555$

$\frac{5}{6}$ is a fraction.

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) ~ $r$

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