1

INDUCTIVE AND DEDUCTIVE REASONING

Prepared by: Ms. Rose Anne B. Camacho

One of the tools used in proving is reasoning.

Deductive Reasoning Inductive Reasoning

2

3

DEDUCTIVE REASONING is a type of logical reasoning that uses accepted facts to reason in a step-by-step manner until we arrive at the desired statement.

4

In deductive reasoning, you assume the hypothesis is true, and then write a series of statements that leads to the conclusion. Each statement is supported by a reason that justifies it.

The set of statements and reasons is called a proof.

5

A proof is a logical argument in which each statement you make is supported/justified by given information, definitions, axioms, postulates, theorems, and previously proven statements.

6

REMEMBER:

POSTULATE is a statement that is accepted without proof.

THEOREM is a statement accepted after it is proved deductively.

7

A simple syllogism is an argument made up of three statements: a major premise, a minor premise (both if which are accepted as true), and a conclusion.

8

EXAMPLE 1:

x: All football players are muscular. y: Joshua is muscular. z: Joshua is a football player

x is the general statementy is the particular statementz is the conclusion

9

EXAMPLE 2:

x: All kangaroos are marsupials. y: All marsupials are mammals.z: All kangaroos are mammals.

10

EXAMPLE 3:

x: The area of a square is the square of the length of its side. y: □ABCD is a square whose side is 5 units. z: The area of □ABCD is 25 units.

11

Do Activity 7: Cubra Cube page 301 of your manual.

12

INDUCTIVE REASONING take specific examples to make general a rule.

In this kind of reasoning, you look for patterns among a set of data and use these patterns to make an educated guess. This educated guess is called a conjecture.

13

Note that the conjecture derived from inductive reasoning might be true, but it is not necessarily true.

14

EXAMPLE 1: Fill in the blanks. Describe the pattern you find.

a. 1, 4, 10, 19, ___, ___, ___b. 1, 3, 6, 10, ___, ___, ___

31 46 6415 21 28

a. Add 12, 15, and 18 b. Add 5, 6, and 7

15

Inductive reasoning may not always lead to the right conclusion. This is because some important factors have been overlooked.

16

Inductive reasoning may not always lead to the right conclusion. This is because some important factors have been overlooked.

17

EXAMPLE 2:

1. 3, 4, 6, 10, 18, ___, ___, ___, 2. 2, 3, 5, 9, 17, ___, ___, ____

34 66 130

33 65 129

18

Do EXERCISE 3 on page 330 of your manual.

Do Activity 2on page 330 of your manual.

19

Reference:

E-Math Third Year pp. 26 – 30 by Oronce Grade 8 Learner’s Manual