1. To solve problems by looking for a pattern
2.3 Deductive Reasoning
OBJ: To use the Law of Detachment & the Law of Syllogism in deductive reasoning
To solve problems by looking for a pattern

2. Inductive vs. Deductive Reasoning
Inductive reasoning- logical conclusions based on several observations
Deductive reasoning- logical conclusions based on a general case

3. Activity 1: Pick a # Add 5 Double the result Subtract 4 Divide in half
Subtract the # started w/
What’s your end result?

4. Activity 2: Follow directions from activity 1 Pick a # N Add 5 N + 5
Double
Subtract 4
Divide in half
Subtract 1st # N
N + 5
2(N + 5) = 2 N + 10
2 N + 6
N + 3 3

5. Looking For A Pattern Find the # of angles formed by 10 distinct rays.
There are many possibilities so let’s work a few and then see if we can develop a pattern
# Rays
# angles 1 2 3 4 5 6 7 8 9 10 1 3 6 10 15 21 28 36 45

6. Law of Detachment
If P  Q is a true conditional and P is true, then Q is true.
P  Q
P is true
Q is true
Therefore,

7. Law of Syllogism
If P  Q, Q  R are true conditionals, then P  R is also true.
P  Q
Q  R
P  R

8. Example:
If 2 #’s are odd, then the sum is even is a true conditional, and 3 and 5 are odd #’s. Use the law of detachment to reach a logical conclusion.
P : 2 #’s are odd
Q : sum is even
P is true because 3 and 5 are odd
Therefore, the sum of 3 and 5 is even.

9. Example:
If a polygon is a square, then it is a rectangle. If a polygon is a rectangle, then it is a parallelogram. Use the law of syllogism to reach a logical conclusion.
P  Q :
Poly is a square rectangle
Q  R :
Poly is a rectangle  parallelogram
P  R : A square is a parallelogram

10. Example: P  Q Q IS THE STATEMENT VALID OR NOT?
(valid means it follows either one of the law forms)
If I watch TV, then I will not do my homework and I did my homework.
P  Q Q
Invalid. The format is detachment, and it doesn’t fit.

11. Your Turn: Is this statement valid?
If a # is a multiple of 20, then it is a multiple of 5. Sam’s locker # is a multiple of 5. Therefore, Sam’s locker is a multiple of 20.
P  Q
INVALID Q P

12. Homework:
Put this in your agenda Pg