1. Do Now: Name each point , line, and line segment, or ray
Understand the fundamentals of propositional logic, arguments, and methods of proof.
Do Now:
Name each point , line, and line segment, or ray
Today’s Agenda
Success Criteria:
Do Now
Lesson
Hand out
Exit Ticket
I can use fundamental propositional logic, arguments, and methods of proofs

2. HW Questions ?

3. What is a statement?

4. Conditional statements
Form of conditional statement:
If p then q (p implies q)
Denote by
p is called hypothesis, q is called conclusion
Ex: If Bobcats win this game,
then they will be number one.

5. Hypothesis: The part of the conditional statement that follows the “IF”
Conclusion: The part of the conditional statement that follows the “THEN”

6. There are two laws of deductive reasoning.
Law of Detachment
If p  q is a true statement and p is true, then q is true.

7. Logic Laws
Objective
Apply the Law of Detachment and the Law of Syllogism in logical reasoning.
Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true.
logic
Deductive reasoning is the process of using __________to draw conclusions from given ________, ________________, and ___________________.
definitions
facts
properties

8. Example 1
Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.
At Reagan High School, students must pass Geometry before they take Algebra 2. Emily is in Algebra 2, so she must have passed Geometry.
Sally is taking the bus to school. She notices that the next 5 people who get on the bus are wearing jeans. She concludes that the next person to get on the bus will also be wearing jeans.
Kim knows she is younger than Jeff, but she is older than Phil. So Kim concludes that Jeff must be older than Phil.

9. Suzie's car is a Chevrolet.
Example 2
Use the Law of Detachment to determine the conclusion.
If a car is a corvette, then it is a Chevrolet.
Suzie's car is a Corvette.
Conclusion
Suzie's car is a Chevrolet.

10. Determine if the conjecture is valid by the Law of Detachment.
Example 3
Determine if the conjecture is valid by the Law of Detachment.
Given: In the World Series, if a team wins four games, then the team wins the series. The Red Sox won four games in the World Series.
Conjecture: The Red Sox won the 2004 World Series.
In the World Series, if a team wins four games, then the team wins the series.
hypothesis
conclusion
The Red Sox won four games in the 2004 World Series
hypothesis
The Red Sox won the 2004 World Series.
conclusion
The conjecture is valid.

11. Determine if the conjecture is valid by the Law of Detachment.
Example 4
Determine if the conjecture is valid by the Law of Detachment.
Given: If a student passes his classes, the student is eligible to play sports. Ramon passed his classes.
Conjecture: Ramon is eligible to play sports.
If a student passes his classes, then the student is eligible to play sports.
The statement “Ramon passed his classes” matches the hypothesis of a true conditional. By the Law of Detachment, Ramon is eligible to play sports. The conjecture is valid.

12. Determine if the conjecture is valid by the Law of Detachment.
Example 5
Determine if the conjecture is valid by the Law of Detachment.
Given: If the side lengths of a triangle are 5 cm, 12 cm, and 13 cm, then the area of the triangle is 30 cm The area of ∆PQR is 30 cm2.
Conjecture: The side lengths of ∆PQR are 5cm, 12 cm, and 13 cm.
If the side lengths of a triangle are 5 cm, 12 cm, and 13 cm, then the area of the triangle is 30 cm2.
The given statement “The area of ∆PQR is 30 cm2” matches the conclusion of a true conditional. But this does not mean the hypothesis is true. The dimensions of the triangle could be different. So the conjecture is not valid.

13. HW #2 Logic Works sheet Odds Pick four problems from each page
Total of twelve

14. Law of Syllogism
If p  q and q  r are true statements, then p  r is a true statement.

15. Example 6
Determine if the conjecture is valid by the Law of Syllogism.
Given: If a figure is a kite, then it is a quadrilateral.
If a figure is a quadrilateral, then it is a polygon.
Conjecture: If a figure is a kite, then it is a polygon.

16. Example 7
Determine if the conjecture is valid by the Law of Syllogism.
Given: If a number is divisible by 2, then it is even.
If a number is even, then it is an integer.
Conjecture: If a number is an integer, then it is divisible by 2.

17. Put the following statements in order.
Example 8
Put the following statements in order.
Given: If an animal is a mammal, then it has hair.
If an animal is a dog, then it is a mammal.
Conclusion? __________________________________________________
__________________________________________________
Law of logic? _________________________________________________
If an animal is a mammal, then it has hair.
If an animal is a dog, then it is a mammal.

18. Example 9
Put the following statements in order.
Then use the Law of Syllogism to draw a conclusion.
a. If quompies plaun, then romples gleer.
b. If homblers frain, then quompies plaun.
c. If ruskers bleer, then homblers frain.
c. If ruskers bleer, then homblers frain.
b. If homblers frain, then quompies plaun.
a. If quompies plaun, then romples gleer.
Conclusion? ________________________________________
__________________________________________________

19. Example 10
Draw a conclusion from the given information.
Given: If 2y = 4, then z = –1. If x + 3 = 12, then 2y = 4. x + 3 = 12
Conclusion? ______________________________________________________________________
b. Given: If a polygon is a triangle, then it has three sides. If a polygon has three sides, then it is not a quadrilateral. Polygon P is a triangle.
Conclusion? _______________________________________________________________________

20. c. Given: If n is a natural number, then n is an integer. If n is an integer, then n is a rational number is a rational number.
Conclusion? _______________________________________________________ ________________________