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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…”
ScienceUsing 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 StudiesTo be elected President you must obtain at least 270 electoral votesGeorge Bush won 287 electoral votesTherefore George Bush is the President.
MathScott 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.
EnglishWhen 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.