Embed Size (px)
Citation preview
Inductive Versus Deductive Reasoning
Free Powerpoint TemplatesPage 4
Inductive Versus Deductive ReasoningInductive Versus Deductive Reasoning
There are two approaches to furthering knowledge
1.reasoning from known ideas and
2. synthesize observations.
Free Powerpoint TemplatesPage 5
Inductive Versus Deductive ReasoningInductive Versus Deductive Reasoning
In inductive reasoning you observe the world, and attempt to explain based on your observations.
You start with no prior assumptions.
Deductive reasoning consists of logical assertions from known facts.
19 Apr 2023
a.reaching a conclusion based on previous observation.
b. It moves from the specific to the general
Types of reasoning
INDUCTIVE REASONING
1² = 1 1 ≤ 12² = 4 2 ≤ 43² = 9 3 ≤ 9(-1)² = 1 -1 ≤ 1
BASED ON THE GIVEN EXAMPLES, DRAW A CONCLUSION/S.
19 Apr 2023
Examples
1² = 1 1 ≤ 12² = 4 2 ≤ 43² = 9 3 ≤ 9(-1)² = 1 -1 ≤ 1
Types of reasoning
BASED ON THE EXAMPLES, WE
NOTICED A PATTERN FROM
WHICH WE DRAW A
CONCLUSIONS.
19 Apr 2023
Examples
1² = 1 1 ≤ 12² = 4 2 ≤ 43² = 9 3 ≤ 9(-1)² = 1 -1 ≤ 1
Types of reasoning
THROUGH INDUCTIVE
REASONING, IT MAY BE CONCLUDED
THAT WHENEVER A
NUMBER IS SQUARED, THE
RESULT IS A NUMBER WHICH IS GREATER THAN OR
EQUAL TO THE ORIGINAL NUMBER.
19 Apr 2023
Examples
1² = 1 1 ≤ 12² = 4 2 ≤ 43² = 9 3 ≤ 9(-1)² = 1 -1 ≤ 1
Types of reasoning
Inductive reasoning is making
conclusions based on patterns you
observe.
The conclusion you reach is called a
conjecture
19 Apr 2023
a. reaching a conclusion based on previous observation.
Types of reasoning
INDUCTIVE REASONING
b. Conclusions are probably TRUE but not necessarily TRUE.
19 Apr 2023
2² = 4 2 ≤ 43² = 9 3 ≤ 9(-1)² = 1 -1 ≤ 1
Consider this example
(½) ²= ¼ ½> ¼Does the
conclusion hold true?
Types of reasoning
Conclusion:
No. Because ½ is greater than ¼.
“WHENEVER A NUMBER IS
SQUARED, THE RESULT IS A
NUMBER WHICH IS GREATER
THAN OR EQUAL TO THE
ORIGINAL NUMBER.”
“WHENEVER A NUMBER IS
SQUARED, THE RESULT IS A
NUMBER WHICH IS GREATER
THAN OR EQUAL TO THE
ORIGINAL NUMBER.”
19 Apr 2023
a. reaching a conclusion based on previous observation.
Types of reasoning
INDUCTIVE REASONING
b. Conclusions are probably TRUE but not necessarily TRUE.
A BEGINNING OBSERVER OF AMERICAN BASEBALL MAY CONCLUDE, AFTER
WATCHING SEVERAL GAMES, THAT THE GAME IS OVER AFTER 9 INNINGS. HE
WILL ONLY REALIZE THAT THIS OBSERVATION IS FALSE AFTER
OBSERVING A GAME WHICH IS TIED AFTER 9 INNINGS.
Another example
19 Apr 2023
INDUCTIVE REASONING IS USEFUL BUT NOT CERTAIN.
THERE WILL ALWAYS BE A CHANCE THAT THERE IS AN
OBSERVATION THAT WILL SHOW THE REASONING TO BE FALSE.
Types of reasoning
INDUCTIVE REASONNG
ONLY ONE OBSERVATION IS NEEDED TO PROVE THE CONCLUSION TO BE
FALSE.
19 Apr 2023
Look carefully at the following figures. Then, use inductive reasoning to make a conjecture about
the next figure in the pattern
Types of reasoning
If you have carefully observed the pattern, may be you came up with the figure below:
19 Apr 2023
Look at the patterns below. Can you draw the next figure or next set of dots using inductive
reasoning?
Types of reasoning
The trick is to see that one dot is always placed between and above two dots. Also, the next figure always has one more dot at the very
bottom rowkeeping this in mind, your next figure should
look like this:
19 Apr 2023
Inductive reasoning is used often in life.
Polling is an example of the use of inductive reasoning.
If one were to poll one thousand people, and 300 of those people selected choice A, then one would infer that 30% of any population might also select choice A. This would be using inductive logic,
because it does not definitively prove that 30% of any population would select
choice A.
Types of reasoning
19 Apr 2023
a. reaching a conclusion by combining known truths to create a new truth
Types of reasoning
DEDUCTIVE REASONNG
b. deductive reasoning is certain, provided that the previously known truths are in fact true themselves.
19 Apr 2023
1. An angle is congruent to itself.
Types of reasoning
Examples
2. Mr. Samuel M. Gier is a math teacher.
3. If 2x = 8, then x = 4.
19 Apr 2023 Types of reasoning
FORMS OF DEDUCTIVE REASONNG
There are a few forms of deductive logic. One of the most common deductive logical arguments is modus ponens, which states
that:
p ⇒ q read as “If p, then q”.
p ∴ q read as “p, therefore q”
19 Apr 2023
If I stub my toe, then I will be in pain.
I stub my toe.Therefore, I am in pain.
Types of reasoning
Example of modus ponens
19 Apr 2023 Types of reasoning
FORMS OF DEDUCTIVE REASONNG
Another form of deductive logic is modus tollens, which states the
following.
p ⇒ q read as “If p, then q”.
¬q ∴ ¬p read as “not q, therefore not p”
19 Apr 2023
If today is Thursday, then the cafeteria will be serving burritos.
The cafeteria is not serving burritos, therefore today is not Thursday.
Types of reasoning
Example of modus tollens
19 Apr 2023 Types of reasoning
FORMS OF DEDUCTIVE REASONNG
Another form of deductive logic is known as the If-Then Transitive Property. Simply put, it means that there can be chains of logic where one thing implies another thing. The If-Then Transitive Property states:
p ⇒ q read as “If p, then q”.(q ⇒ r) (∴ p ⇒ r)read as ((If q, then r), therefore (if p, then r))
19 Apr 2023
If today is Thursday, then the cafeteria will be serving burritos.
If the cafeteria will be serving burritos, then I will be happy.
Therefore, if today is Thursday, then I will be happy.
Types of reasoning
Example of If-Then Transitive Property
19 Apr 2023
Deductive reasoning is based on laws or general principles.
People using deductive reasoning apply a general principle to a specific example.
Types of reasoning
DEDUCTIVE REASONNG
19 Apr 2023
Use inductive reasoning to form arguments based on
experience. Use deductive reasoning to
form arguments based on rules or previously known
facts.
Types of reasoning
Choosing a Strategy
Answer orally
19 Apr 2023
All vegetables are good for you.
Broccoli is a vegetable. Therefore, broccoli is
good for you. This is an example of what type of
reasoning?
Types of reasoning
EXERCISES
DEDUCTIVE REASONING
19 Apr 2023
Broccoli is a vegetable.Broccoli is a green.
Therefore, all vegetables are green.
Why is this conclusion invalid?
Types of reasoning
EXERCISES
PROOF
KINDS OF PROOF
HOMEWORK
Give two examples using deductive and inductive reasoning.
Write your answers in a paper (one-half crosswise)
