Warm-Up

1
Warm-Up

• State whether the following arguments MUST be
  true.
• If it is Friday, then Kendras family has pizza
  for dinner. Today is Friday, therefore, Kendras
  family will have pizza for dinner.
• If the ipod is on then the volume is loud. If the
  volume is loud then the teachers will complain.
  The ipod is on so other students are complaining.
  

2
Section 2.4 Deductive Reasoning

• SWBAT use the Law of Detachment and the Law of
  Syllogism

3
Inductive vs. Deductive Reasoning

• Inductive reasoning uses previous examples and
  patterns to form a conjecture
• Deductive reasoning uses facts, definitions, and
  properties to write a logical argument

4
Example

• Luke knows that Casandra is a sophomore and
  Nicole is a junior. All the other juniors that
  Luke knows are older than Casandra. Therefore,
  Luke reasons that Nicole is older than Casandra.

5
Example

• Logan knows that Alex is older than Myranda. He
  also knows that Myranda is older than Kelsea.
  Logan reasons that Alex is older than Kelsea.

6
Law of Detachment

• If p ? q is a true conditional statement and p is
  true, then q is true

7
Example

• If Levi misses a practice the day before a game,
  then he will not be a starting player in the
  game.
• Levi misses practice on Tuesday and there is a
  game on Wednesday
• Therefore, Levi will not be a starting player at
  the game on Wednesday

8
Example

• Determine if the following argument follows the
  Law of Detachment.
• If you came from Mrs. Ambs Algebra class, then
  you are very smart.
• Jenny came from Mrs. Ambs Algebra class
• Therefore, Jenny is very smart

9
Example

• Determine if the following argument follows the
  Law of Detachment.
• If you studied for the Chapter 1 test, then you
  did very well.
• Brooke studied for the Chapter 1 test.
• Therefore Brooke did the best in the class

10
Try it on your own!

• Write an example and a non-example of the Law of
  Detachment

11
Law of Syllogism

• If p ? q and q ? r are true conditional
  statements, then p ? r is true.

12
Example

• If you are tired then you work too hard
• If you work too hard then you need more sleep
• Therefore,
• if you are tired then you need more sleep

13
Example

• If possible, use the Law of Syllogism to draw a
  conclusion from the given conditionals
• If you are 16, then you can drive
• If you can drive, then you have your license

14
Example

• If possible, use the Law of Syllogism to draw a
  conclusion from the given conditionals
• If a bird is the fastest bird on land, then it is
  the largest of all birds
• If a bird is the smallest bird, then it has a
  nest the size of a walnut half-shell

15
Try it on your own!

• Write an example and a non-example of the Law of
  Syllogism.

16
Detachment and Syllogism

• You can use the Law of Syllogism and the Law of
  Detachment together to make conclusions

17
Example

• If you live in Accra, then you live in Ghana.
• If you live in Ghana, then you live in Africa.
• Aissa lives in Accra.