Download Lesson 2-4 Deductive Reasoning

Do Now:
1. True
2. False
C
D
3. False
Lesson 2-4:
Deductive Reasoning
Goal: Use the Law of Detachment and the law of Syllogism.
Laws of Logic:
• Law of Detachment:
• If the hypothesis of a true if-then statement is true, then the
conclusion is also true.
• Ex:
If you are late for your interview, you will probably not
be offered the job.
You are late for your interview.
• By the Law of Detachment we can conclude that you will
probably not be offered the job.
Example 1:
.
Using the Law of Detachment
• What can you conclude from the given true statements?
• If a student gets and A on a final exam, then the student will pass the
course.
Felicia got an A on her history final.
• If a ray divides an angle into two congruent angles, then the ray is an
angle bisector.
𝑅𝑆 divides ∠𝐴𝑅𝐵 so that ∠𝐴𝑅𝑆 = ∠𝑆𝑅𝐵
• If two angles are adjacent, then they share a common vertex.
∠1 𝑎𝑛𝑑 ∠2 share a common vertex.
Laws of Logic:
• Law of Syllogism:
• If statement p, then statement q.
If statement q, then statement r.
If statement p, then statement r.
• Ex:
If these statements are true,
then this statement is true.
If Naomi saves enough money, she can buy a concert
ticket.
If she buys a concert ticket, she can see her favorite
band.
• So it follows from the Law of Syllogism that If Naomi saves
enough money, she can see her favorite band.
Example 2:
Using the Law of Syllogism
• What can you conclude from the given information?
• A) If a figure is a square, then the figure is a rectangle.
If a figure is a rectangle, then the figure has four sides.
If a figure is a square, then the figure has four sides.
• B) If you do gymnastics, then you are flexible.
If you do ballet, then you are flexible.
Example 3: Using the Laws of
Syllogism and Detachment.
• What can you conclude from the given information?
• If you live in Cincinnati, then you live in Ohio.
• If you live in Ohio, then you live in the United States.
• Ken lives in Cincinnati.
Ken Lives in the United States
Checkpoint:
The midpoint of 𝐴𝐵 is at (2, 0).
Checkpoint:
If the perimeter of a square is 20 feet, then the area is 25 square feet.
Assignment:
• Pp 110 – 112 #’s 6 – 32 even