Deductive Reasoning

Deductive reasoning is the process of reasoning logically

from given statements to a conclusion.

Deductive Reasoning Is…

• 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.

For Example

All dogs have a tail.

Buddy is a dog.

Therefore Buddy has a tail.

Deductive Vs. Inductive

• Induction is usually described as moving from the specific to the general, while deduction begins with the general and ends with the specific.

• Arguments based on laws, rules and accepted principles are generally used for Deductive Reasoning. Observations tend to be used for Inductive Arguments.

Still don’t get it?• 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 1: I am a professor at the University, I teach deductive

reasoning. • Man: Deductive reasoning? What is that? • Neighbor 1: 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 1: The fact that you have a dog, leads me to deduce that

you have a family. • Man: Right again. • Neighbor 1: Since you have a family I deduce that you have a wife. • Man: Correct. • Neighbor 1: And since you have a wife, I can deduce that you are

heterosexual. • Man: Yup. Neighbor 1: That is deductive reasoning!

• Who is known for using Deductive Reasoning?

Sherlock Holmes

• Sherlock Holmes would use deductive reasoning to help solve crimes.

Andrew Ault

Example:

Sherlock Holmes could help solve a mystery by making inferences. If Holmes saw a pack of cigarettes by a victim (the victim did not smoke), Holmes can make the assumption that the killer is a smoker.

However…

• Deductive reasoning may not be the most accurate way of solving a problem, cause we all know that assumptions can be wrong.

Other faults of deductive reasoningAll Graduates of M.I.T. are EngineersGeorge is not from M.I.T.Therefore George is not an Engineer

Everybody from Texas is a cowboyScott is from TexasScott is a cowboy

My sociology teacher told us that those of us who grew up in America in the twentieth century, with all of its greed, bigotry, and abuse of power inherited a sickness. Well, if I’m sick, I guess I don’t have to go to school today.

How Can Deductive Reasoning Be Applied In School?

“Ugggh, I don’t know…”

Science

Using laws and rules to make assumptions

The law of gravity means everything that goes up must come downI threw a baseball in the airThat means the baseball must come down.

Social Studies

To be elected President you must obtain at least 270 electoral votesGeorge Bush won 287 electoral votesTherefore George Bush is the President.

Math

Scott has a case of soda in his house since there are 13 cans of soda left I deduce that Scott has drank 11 cans of soda.

English

When I see like in a sentence, I deduce that it is a simile.

What professions do you think commonly use Deductive

Reasoning?

Why?• These professions tend to ask a lot of questions to try

to solve problems or to prove a point.• Often they would have to make assumptions to solve

problems.• They would use rules and widely accepted beliefs to

prove their argument.

For example:An attorney states that his client is innocent because the crime victim was hit by a car. Since his client does not have a license. He can deduce that his client is innocent.

An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion will she make?

The mechanic can conclude that the car will not start.

If there is lightning, then it is not safe to be

out in the open. Marla sees lightning

from the soccer field.

It is not safe for Marla to be out in the

open.

If it is snowing, then the temperature is less than or equal to 32˚F.

The temperature is 20˚F.

The converse of the original assumption is not true, so

It is not possible to conclude that it is snowing.

If a baseball player is a pitcher, then that

player should not pitch a complete game

two days in a row. Brent is a pitcher. On

Monday, he pitches a complete game.

What can you conclude?

Brent either did not pitch a complete

game on Sunday or he should not

pitch a complete game on Tuesday.

If M is the midpoint of a segment, then

it divides the segment into two

congruent segments.

M is the midpoint of .AB

You can conclude that M divides into

two congruent segments, or

AB

.MBAM

If an angle is obtuse, then it is not acute.

is not obtuse.XYZ

The converse of the assumption is not true, so It is not possible to conclude that is acute.XYZ

If a road is icy, then driving conditions are hazardous.

Driving conditions are hazardous.

The converse of the assumption is not true, so It is not possible to conclude

that the road is icy.

There are three switches downstairs. Each

corresponds to one of the three light

bulbs in the attic. You can turn the

switches on and off and leave them in any

position. How would you identify which

switch corresponds to which light bulb, if

you are only allowed one trip upstairs?

bulbs

Answer

Turn one light switch one.Wait about 20 minutes, then turn it off.

Turn another light on, and proceed upstairs.One light should be on,

Two lights are off- however, one light is hot and one is cold.