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.
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.
Andrew Ault
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 reasoning
All Graduates of M.I.T. are Engineers
George is not from M.I.T.
Therefore George is not an Engineer
Everybody from Texas is a cowboy
Scott is from Texas
Scott 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 down
I threw a baseball in the air
That means the baseball must come down.
Social Studies
To be elected President you must obtain at least 270
electoral votes
George Bush won 287 electoral votes
Therefore 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 AB into
two congruent segments, or AM  MB.
If an angle is obtuse, then it is not acute.
XYZ is not obtuse.
The converse of the assumption is not
true, so It is not possible to conclude
that XYZ is acute.
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?
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.