free powerpoint templates page 2 inductive versus deductive reasoning

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Inductive Versus Deductive Reasoning

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Inductive Versus Deductive ReasoningInductive Versus Deductive Reasoning

There are two approaches to furthering knowledge

1.reasoning from known ideas and

2. synthesize observations.

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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.

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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.

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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.

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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

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a. reaching a conclusion based on previous observation.

Types of reasoning

INDUCTIVE REASONING

b. Conclusions are probably TRUE but not necessarily TRUE.

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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.”

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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

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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.

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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:

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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:

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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

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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.

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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”

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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

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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”

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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))

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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

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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

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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

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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

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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)