1. Deductive and Inductive Reasoning

2. Problem Solving Logic – The science of correct reasoning.
Reasoning – The drawing of inferences or conclusions from known or assumed facts.
When solving a problem, one must understand the question, gather all pertinent facts, analyze the problem, compare with previous problems (note similarities and differences), and perhaps use pictures or formulas to solve the problem.

3. 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.

4. Examples of Inductive Reasoning
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 fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.

5. Example of Deductive Reasoning
The catalog states that all entering freshmen must take a mathematics placement test.
An Example:
You are an entering freshman.
Conclusion: You will have to take a mathematics placement test.

6. Deductive Reasoning
This method of reasoning produces results that are certain within the logical system being developed.
A type of logic in which one goes from a general statement to a specific instance.
The classic example
All men are mortal. (major premise)
Socrates is a man. (minor premise)
Therefore, Socrates is mortal. (conclusion)
The above is an example of a syllogism.

7. Deductive Reasoning Examples: All students eat pizza.
Claire is a student at CSULB.
Therefore, Claire eats pizza.
2. All athletes work out in the gym.
Barry Bonds is an athlete.
Therefore, Barry Bonds works out in the gym.

8. Deductive Reasoning Examples: All students eat pizza.
Claire is a student at WMHS.
Therefore, Claire eats pizza.
2. All athletes work out in the gym.
Lebron James is an athlete.
Therefore, Lebron James works out in the gym.

9. Deductive Reasoning 3. All math teachers are over 7 feet tall.
Mr. P is a math teacher.
Therefore, Mr. P is over 7 feet tall.
The argument is valid, but is certainly not true.

10. Inductive Reasoning
Inductive Reasoning, involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed.

11. All mammals are warm-blooded. So, all bats are warm-blooded.
All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
All arguments are deductive or inductive.
Deductive arguments are arguments in which the conclusion is claimed or intended to follow necessarily from the premises.
Inductive arguments are arguments in which the conclusion is claimed or intended to follow probably from the premises.
Is the argument above deductive or inductive?

12. All mammals are warm-blooded. So, all bats are warm-blooded.
All bats are mammals.
All mammals are warm-blooded.
So, all bats are warm-blooded.
Deductive.
If the premises are true, the conclusion, logically, must also be true.

13. Kristin is a law student. Most law students own laptops.
So, probably Kristin owns a laptop.
In the example above, the word probably shows that the argument is inductive.