1. Section 1.1 Inductive Reasoning 1/16

2. DEDUCTIVE REASONING Two Types of Reasoning INDUCTIVE REASONING 2/16

3. Deductive Reasoning Facts Rules Truth Proven Theorems Postulates Properties Definitions 3/16

4. Inductive Reasoning Use of Patterns Conjectures Use of Examples Prediction Educated Guesses Generalizations through Patterns 4/16

5. Inductive reasoning is the process of drawing a general conclusion by observing a pattern from specific instances. conclusionhypothesis conjecture This conclusion is called a hypothesis or conjecture. Inductive Reasoning 5/16

6. Inductive Reasoning Ex. #1 FIGURE 1 FIGURE 2 FIGURE 3 How many stars in the figure 4? 6/16

7. Inductive Reasoning Ex. #2 1, 4, 9, 16, 25, ……. What is the next number? 7/16

8. Inductive Reasoning Ex. #3 3, 9, 15, 21, 27, …. What is the next number? 8/16

9. 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? 9/16

10. Inductive Reasoning Ex. #5 2, 4, 8, ……. What is the next number? 10/16

11. Counter Examples Are all conjectures made by a pattern correct & true? How do we disprove a conjecture? We give a COUNTER EXAMPLE!! 11/16

12. Counter Examples Ex. #1 Conjecture: The sum of three consecutive numbers is always odd. Is this conjecture true? Yes or No 12/16

13. 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 13/16

14. 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 14/16

15. Counter Examples Ex. #4 Conjecture: For all real numbers x, the expressions x 2 is greater than or equal to x. Is this conjecture true? Yes or No 15/16

16. HOMEWORK 1.1 P. 6 16 – 23, 34 – 39, 47, 48 16/16