p qp q q pq p p  q ~p  ~q ~q  ~p q p September 17, 2014.

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A Closer Look at Inductive vs. Deductive Reasoning.

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Presentation transcript:

p qp q q pq p p  q ~p  ~q ~q  ~p q p

September 17, 2014

 Logic – The science of correct reasoning.  Reasoning – The drawing of inferences or conclusions from known or assumed facts.  When solving a problem, 1. understand the question 2. gather facts, analyze the problem i.e. compare with previous problems (note similarities and differences), 3. Use pictures or formulas to solve the problem.

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.

Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

1) Every quiz has been easy. Therefore, the test will be easy. 2) The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow. 3) Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.

The catalog states that all entering freshmen must take a mathematics placement test. Conclusion: You will have to take a mathematics placement test. You are an entering freshman.

Inductive or Deductive Reasoning: Definition of perpendicular lines: two lines intersect to form right angles at their intersection. Therefore <AXB is a right angle Deductive Reason: based on a property or definition

What comes next????? Is there a rule? Colored triangle rotating 90° CW in the corners of the square Inductive Reasoning

Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true.

DeductionInduction General  SpecificSpecific  General Based on laws, principles, rules Based on observation

 Man approaches to greet a new neighbor who is just moving into the house next door and asks what he does for a living.  Neighbor: I am a professor at the University, I teach deductive reasoning.  Man: Deductive reasoning? What is that?  Neighbor: Let me give you an example. I see you have a dog house out back. By that I deduce that you have a dog.  Man: That's right.  Neighbor: The fact that you have a dog, leads me to deduce that you have a family.  Man: Right again.  Neighbor: Since you have a family I deduce that you have a wife.  Man: Correct.  Neighbor: And since you have a wife, I can deduce that you are married.  Man: Yup.  Neighbor: That is deductive reasoning!

 Sometimes deductive or inductive reasoning is not the best way… Here’s some faults:  Ex 1: Deductive Reasoning Maybe we made a wrong assumption! Everybody from Texas is a cowboy Scott is from Texas Scott is a cowboy

 Sometimes deductive or inductive reasoning is not the best way… Here’s some faults:  Ex 1: Inductive Reasoning Did we really see the WHOLE pattern?