1. 2-1: Logic with Inductive Reasoning
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2-1: Logic with Inductive Reasoning

2. Logic with Inductive Reasoning
Section 2–1
Geometry PreAP, Revised ©2013
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2-1: Logic with Inductive Reasoning

3. 2-1: Logic with Inductive Reasoning
Directions
Get two sheets of blank computer paper
Staple the front page and put your name on it
DO NOT GO AHEAD. Stapler is going around. Wait for further directions.
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2-1: Logic with Inductive Reasoning

4. Introduction of Inductive Reasoning
Inductive reasoning can be used to make predictions about the future based on the past or to make conjectures about the past based on the present.
Inductive reasoning does not always lead to the truth.
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2-1: Logic with Inductive Reasoning

5. Inductive Reasoning – Page 1
The process of REASONING that a RULE or statement is TRUE because SPECIFIC AREAS are true
Used to form CONJECTURES and to continue patterns, or test hypotheses
Conjecture – is a generalized conclusion (not necessarily correct) Taking something specific to something general
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2-1: Logic with Inductive Reasoning

6. Steps of Inductive Reasoning
Look for a pattern
Make a Conjecture
Prove the Conjecture or provide a counterexample
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2-1: Logic with Inductive Reasoning

7. 2-1: Logic with Inductive Reasoning
Example 1
Make a conjecture about these next two terms:
7, 14, 21, 28, …
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2-1: Logic with Inductive Reasoning

8. 2-1: Logic with Inductive Reasoning
Example 2
The product of an even number and an odd number is ______________.
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2-1: Logic with Inductive Reasoning

9. 2-1: Logic with Inductive Reasoning
Example 3
A scientist takes a piece of salt, turns it over a Bunsen burner, and observes that it burns with a yellow flame. She does this with many other pieces of salt, finding they all burn with a yellow flame. What is the conjecture?
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2-1: Logic with Inductive Reasoning

10. 2-1: Logic with Inductive Reasoning
Your Turn
Write an example of a conjecture about two even numbers and prove it.
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2-1: Logic with Inductive Reasoning

11. Example 4
For the statement, “Every integer of n, n3 is positive” provide a counterexample. To provide if it is false, start plugging in numbers.
Let n = 1.
Since n3 = 1 and 1 > 0, the conjecture holds.
Let n = –2.
Since n3 = –8 and –8 < 0, the conjecture false.
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2-1: Logic with Inductive Reasoning

12. 2-1: Logic with Inductive Reasoning
Example 5
For the statement, “For any real number x, x2 ≥ x.” provide a counterexample.
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2-1: Logic with Inductive Reasoning

13. 2-1: Logic with Inductive Reasoning
Your Turn
For the statement, “Two supplementary angles are not congruent.” provide a counterexample.
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2-1: Logic with Inductive Reasoning

14. 2-1: Logic with Inductive Reasoning
Assignment
Page 77 8, all, 16, 20-23, 25, 28, 31, 37, 38
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2-1: Logic with Inductive Reasoning