Section 1.1Inductive Reasoning

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DEDUCTIVE

REASONING

Two Types of Reasoning

INDUCTIVEREASONIN

G

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Deductive Reasoning

Facts

RulesTruth

Proven Theorems

PostulatesProperties

Definitions

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Inductive Reasoning

Use of Patterns

Conjectures Use of Examples

Prediction

Educated Guesses

Generalizations through Patterns

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Inductive reasoning is the process of drawing a general conclusion by observing a pattern from specific instances.

This conclusion is called a hypothesis or conjecture.

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Inductive Reasoning Ex. #1

FIGURE 1 FIGURE 2 FIGURE 3

How many stars in the figure 4?

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Inductive Reasoning Ex. #2

1, 4, 9, 16, 25, …….What is the next number?

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Inductive Reasoning Ex. #3

3, 9, 15, 21, 27, ….What is the next number?

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Inductive Reasoning Ex. #4

At the school cafeteria Jim notices that for the last 3 Mondays Spaghetti was

served, so using inductive reasoning… what

conjecture might he make?

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Inductive Reasoning Ex. #5

2, 4, 8, …….

What is the next number?

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Counter Examples

Are all conjectures made by a pattern correct & true?

How do we disprove a conjecture?

We give a COUNTER EXAMPLE!!

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Counter Examples Ex. #1

Conjecture:

The sum of three consecutive numbers is always odd.

Is this conjecture true? Yes or No

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Counter Examples Ex. #2

Conjecture:

If a number is divisible by 6, then it is divisible by 3.

Is this conjecture true? Yes or No

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Counter Examples Ex. #3

Conjecture:

The product of two positive whole numbers is always greater than either of the two numbers.

Is this conjecture true? Yes or No

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Counter Examples Ex. #4

Conjecture:

For all real numbers x, the expressions x2 is greater than or equal to x.

Is this conjecture true? Yes or No

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HOMEWORK 1.1

P. 6 16 – 23, 34 – 39, 47, 48

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