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Logic - PowerPoint PPT Presentation

Logic. Sentences, Statements and Truth Values. Unit 1. Logic. - the science of reasoning. Mathematical sentences. declarative statements that may be either true or false (has a truth value ). The Ravena Library is on Main Street. mathematical sentence. 17 + 5 = 21.

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Logic

Sentences, Statements and Truth Values

Unit 1

Geometry

- the science of reasoning

Mathematical sentences

declarative statements that may be either true or false (has a truth value).

The Ravena Library is on Main Street.

mathematical sentence

17 + 5 = 21

mathematical sentence

Not a mathematical sentence

Not a mathematical sentence

14 – 8 = 6

mathematical sentence

Every parallelogram

Not a mathematical sentence (it’s a phrase)

- sentences that contain a

variable

What is the variable of each sentence?

x + 2 = 8

the variable is x

He broke my pencil.

the variable is he

Jenny found it behind the sofa.

the variable is it

- the set of all elements that are possible replacements for the variable.

Solution set (truth set)

- the elements from the domain that make an open sentence true.

Open sentence:

It is the third month of the year.

It

Variable:

Domain:

{all the names of the months}

Solution (truth) set:

{March}

- a statement that can’t be judged as

true or false. There are no variables.

Negations

The negation of a statement always has the opposite truth value of the original statement.

Insert or take out the word ‘not’ to obtain the negation of a statement.

For example:

Statement: Neil Armstrong walked on the moon.

True

Negation: Neil Armstrong did not walk on the moon.

False

For example:

Statement: A duck is not a mammal.

True

Negation: A duck is a mammal.

False

mathematical sentence or not.

1. Thanksgiving is on the fourth Thursday in November.

Mathematical Sentence

2. Where did you go?

Not a Mathematical Sentence

3. Be quiet.

Not a Mathematical Sentence

4. y – 7 = 3y + 4

Mathematical Sentence

5. The first president of the United States was Abraham Lincoln.

Mathematical Sentence

5. She is tall.

6. 2y > 17

7. This country has the third largest population.

8. It is my favorite food.

9. The Statue of Liberty was given to the United States by France.

True

10. Tallahassee is a city in Montana.

False

11. 6x + 4 = 16

Open

Variable: x

12. 6(2) + 4 = 16

True

using the replacement set

13. Its capital is Albany.

{New York}

14. It is on the east coast of the United States.

{Massachusetts, New York}

16. It is one of the last two states admitted to the United States.

20. A stop sign is painted green.

F

T

A stop sign is not painted green.

21. There are 1,760 yards in a mile.

T

F

There are not 1,760 yards in a mile.

22. 14(2) – 16 = 12

T

F

14(2) – 16 ≠ 12

23. Today is not Thursday.

F

T

Today is Thursday.

Worksheet

Sentences, Statements, and Truth Values

1.01