2.1 Using Inductive Reasoning to Make Conjectures.

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2.1 Using Inductive Reasoning to Make Conjectures

Find the pattern  If everyone at a party of people shakes everyone else’s hand one time, how many handshakes will there be?  January, March, May ____________  7,14,21,28,_________  1,2,4,__________  ____________ people ….20 Hand- shakes

Inductive Reasoning  When several examples form a pattern and you assume or draw the conclusion that the pattern will continue (like on the previous slide) you are applying inductive reasoning.  Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true.

Conjecture  A statement you believe to be true based on inductive reasoning.  Examples: The product of an even number and an odd number is ________. The product of an even number and an odd number is ________. The sum of two odd numbers is ________. The sum of two odd numbers is ________.

How do you show that a conjecture is always true? PROVE IT!!!

How do you show that a conjecture is false? Find a counterexample.

Counterexamples can be…..  A drawing  A statement, or  A number.

True or False?  If x = 3, then x² = 9.  If x² = 9, then x = 3.  For every integer, n³ is positive.  If the grass is wet, then it rained.  If B is the midpoint of AC, then AB = BC.  If AB = BC, then B is the midpoint of AC.  For any real number x, x² > x.  The winner of the door decoration contest will get a pizza party! ~ ~ _

Inductive Reasoning Look for a pattern Make a conjecture Is it true? If yes, PROVE IT! If no, provide a Counterexample.