1. Inductive and Deductive Reasoning
Lesson 1-1
Inductive and Deductive Reasoning

2. Inductive Reasoning- the process of arriving at a general conclusion based on observations of specific examples.
We can never be certain that these conclusions are true.
For this reason conclusions are called conjectures, hypotheses, or educated guess.

3. If there is just one case for which the conjecture does not hold, then the conjecture is false. Such a case in a counterexample.
Inductive reasoning can help reveal patterns about numbers.

4. Identify the pattern to find the next number.
3, 12, 21, 30, 39
3, 12, 48, 192, 768
3, 4, 6, 9, 13, 18

5. Sometimes you will have to look at the digits that immediately precede it.
1,1,2,3,5,8,13,21,

6. Deductive Reasoning – proving a specific conclusion from one or more general statements
The conclusion that is proved true is called a theorem.

7. Consider the following procedure:
Select a number. Multiply the number by 6. Add 8 to the product. Divide this sum by 2. Subtract 4 from the quotient.
Repeat this procedure for 4 different numbers and write a conjecture
Represent the original number by n and use deductive reasoning to prove the conjecture

8. Assignment: 2 – 50, 52, 56 even on pg 9-11