1. Geometry
Logic

2. Logic What is Logic? It is our ability to reason.
It is the foundation of sound thinking.

3. Where do we start?
I start with the question:
What is a sentence?
Every good sentence needs a noun or subject, an action word or a verb and an object or the completion of the idea of the sentence.

4. How is a mathematical sentence different from an grammatical sentence?
A mathematical sentence has a certain truth value. It is called a closed sentence.
A sentence whose truth value is uncertain is called an open sentence.

5. Negation
The negation of a sentence changes the truth value of the original sentence.
It is represented by the symbol ~.
If p represents my sentence
then ~p represents it’s negation.

6. Try This In the space provided write a sentence in words.
Then write the negation of that sentence in words.

7. Logical Connectors
A conjunction connects two simple sentences using the word “and “ to make a compound sentence.
Given the two simple sentences
Sara goes swimming.
Tom is a life guard.
The conjunction would be
Sara goes swimming and Tom is a life guard

8. Logical Connectors with symbols
The word And is represented by the symbol 
Example
Let p represent: Sara goes swimming.
Let q represent: Tom is a life guard.
Sara goes swimming and Tom is a life guard.
Would be represented by:
pq

9. The compound sentence p  q is only true when both individual sentences are true.F

10. Disjunction Connective
A disjunction connects two simple sentences using the word “or “ to make a compound sentence.
Given the two simple sentences
Sara will study
Sara goes to the movies
The compound sentence would be
Sara will study or Sara goes to the movies

11. Using Symbols The connector “or” is represented by the symbol “.”
Example:
Let p represent: Sara will study
Let q represent: Sara goes to the movies
Sara will study or Sara will go to the movies. represents:
p  q

12. The disjunction
p  q is only false when both p and q are false. p q
p  q T F

13. A conditional is a compound sentence usually formed by the words if…
A conditional is a compound sentence usually formed by the words if….then to combine 2 simple sentences. The  is used to represent if…then.
Given the simple sentences
John studies
John gets good grades
The compound sentence would be:
If John studies then John gets good grades.

14. Using Symbols A conditional statement is also called an implication
p implies q.
Let p represent: John studies
Let q represent: John gets good grades
If John studies then John gets good grades.
Represent by: p  q

15. In a conditional statement the p sentence is called the hypothesis or the premise and the q sentence is called the conclusion.

16. The conditional statement is only false when a true hypothesis implies a false conclusion.q
p q T F

17. Homework In the text book Pg. 41 Numbers 48-61 Pg. 47 Numbers 13-20