1.2 Inductive Reasoning

Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?

Inductive Reasoning When you make a conclusion based on a pattern of examples or past experience, you are using inductive reasoning. Inductive reasoning: looking for patterns and making observations

Conjecture Conjecture: an unproven statement that is based on a pattern or observation Ex: The sum of two odd number is _________ = = = = = 30 Conjecture: The sum of any two odd numbers is even.

Conjectures The difference of any two odd numbers is _______. The difference of any two odd numbers is even.

Stages of Inductive Reasoning 1.Look for a pattern. Look at several examples. 2.Make a conjecture. Use examples to make a general conjecture. Change it if needed. 3.Verify the conjecture. Use logical reasoning to verify that the conjecture is true in all cases.

Counterexamples A conjecture is an educated guess. – Sometimes it is true and other times it is false – True for some cases does not prove true in general – To prove true, have to prove true in all cases – Considered false if not always true. – To prove false, need only 1 counterexample Counterexample: an example that shows a conjecture is false.

Counterexamples Conjecture: If the product of two numbers is even, the numbers must be even. Counterexample: 7 × 4 =28 28 is even but 7 is not

Counterexamples Conjecture: Any number divisible by 2 is divisible by 4. Counterexample: 6 is divisible by 2, but not by 4.

Review What is a conjecture? – An unproven statement that is based on a pattern or observation How can you prove a conjecture is false? – By finding just one counterexample.