Section 2.1: Use Inductive Reasoning Conjecture: A conjecture is an unproven statement that is based on observations; an educated guess. Inductive Reasoning: Your reasoning is considered inductive when you use observations, patterns, or specific examples to make a conjecture.

Example Make a conjecture about the pattern you see below. -5, 15, -45, 135, -405, … To get from one number to the next you multiply by -3.

Example Make a conjecture about the product of any three negative numbers. The product of any three negative numbers will be a negative number.

Disproving a Conjecture Inductive reasoning can never be used to prove without a doubt that a conjecture is true. But, disproving a conjecture (proving it false) can be done by finding any one specific example where the conjecture fails to be true, called a counterexample.

Example Find a counterexample to show the following conjecture is false. Conjecture:The value of x 2 is always greater than the value of x. Counterexample:If x = 1, x 2 = 1 which is not greater than 1.

Example Is the following conjecture true or false? If false show a counterexample. Conjecture:If x is an integer, then x 2 is positive. False. If x = 0, then x 2 = 0 which is not positive.

One More Example Given that WX = XY, would it be true to conjecture that W, X, and Y are collinear? Explain. False. W, X, and Y do not have to be collinear. X8 WYWY