Entry Task

Using Deductive Reasoning2.4

Learning Target:Given a true statement I can use

deductive reasoning to make valid conclusions

• Deductive Reasoning –(aka logical reasoning) a process of reasoning logically from given facts to a conclusion

A mechanic uses deductivereasoning to determine whatis wrong with your car.

2-3 Using Deductive Reasoningto Verify Conjectures

A doctor will use deductive reasoning to diagnose apatient.

2-3 Using Deductive Reasoningto Verify Conjecture

A lawyer uses deductive reasoningto build a case.

2-3 Using Deductive Reasoningto Verify Conjectures

A construction foreman usesdeductive reasoning to determinewhat materials are needed ata work site.

2-3 Using Deductive Reasoningto Verify Conjectures

And of course adetective uses deductive reasoning to solve crimes.

2-3 Using Deductive Reasoningto Verify Conjectures

Deductive Reasoning

The process of reasoning using logic to draw Conclusion from given facts, definitions, and properties AKA logical reasoning.

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.

Day 1

Examples of Inductive Reasoning

Some examples

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.

Deductive Reasoning

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.

An Example:

Day 1

Deductive Reasoning

There are two laws used in logical reasoning:

LAW OF DETACHMENT

LAW OF SYLLOGISM

Law of Detachment

Deductive Reasoning

LAW OF DETACHMENTThis law states that if a conditional statement is true, andIts hypothesis is true, then its conclusion is true.

Example: If it is raining outside, then I will use my umbrella.

It is raining outside

What can you conclude?

I will use my umbrella.

If p q is a true statement and p is true,Then q is true.

Day 1

Law of Syllogism

Deductive Reasoning LAW OF SYLLOGISM

If Tony goes to the movies, then he will eat popcorn.

If Tony eats popcorn, he will get indigestion.

Conclusion: If Tony goes to the movies, then he will getIndigestion.

p q

q r

p r

Let’s Check • If possible make a conclusion…..• 1) If it is Tuesday, then you will go bowling.

You go bowling.

• 2) If it is Saturday then you walk to work. If you walk to work then you wear your sneakers.

No, you can’t make a conclusion. The last statement relates to the conclusion and not the hypothesis.

Yes, if it is Saturday, then you wear sneakers.

Homework

• Homework: P. 110 #7-29 odds not 25

• Challenge – 32