1. LG 1: Logic A Closer Look at Reasoning

2. Deductive vs. Inductive Reasoning
The difference:
inductive reasoning uses patterns to arrive at a conclusion (conjecture)
deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion.

3. Conjectures and Counterexamples
Conjecture is an educated guess based on information given
Counterexample is an example that proves a conjecture is false.

4. Examples of Inductive Reasoning
Some examples – What is conjecture and can you think of a counterexample?
Every quiz has been easy. Therefore, the test will be easy.
The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow.
Every bird I have seen flies. Therefore all birds must fly.

5. Two Types of Deductive Reasoning
Law of Detachment
Law of Syllogism

6. Deductive Reasoning LAW OF DETACHMENT
This law states that if a conditional statement is true, and
Its hypothesis is true, then its conclusion is true.
Example: If it is raining outside, then I will use my umbrella.
What can you conclude?
It is raining outside
I will use my umbrella.

7. Law of Detachment All sophomores must take Geometry. You are sophomore
Another Example:
All sophomores must take Geometry.
You are sophomore
Conclusion: You will take Geometry.

8. Law of Syllogism
If the conclusion of one statement is the same as the hypothesis of the next statement, you can eliminate these statements.
If A, then B
If B, then C
If A, then C

9. Law of Syllogism
Example: If it rains outside, the walkway will get wet.
If the walkway is wet, the walkway will be slippery.
What can we conclude from the Law of Syllogism?
If it is raining, the walkway will be slippery.

10. You Try!
If a figure is a rectangle, then it is a parallelogram.
If a figure is a parallelogram, then its diagonals bisect each other.
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11. Inductive or Deductive Reasoning?
Geometry example…
60◦ x
What is the measure of angle x?
The sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30°

12. Inductive or Deductive Reasoning?
Geometry example…
What is the next shape in the sequence?