2-1: Logic with Inductive Reasoning Grade Distribution 1st 2nd 6th 7th A B C D F 100+ No Shows Avg 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

Logic with Inductive Reasoning Section 2–1 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Directions Get two sheets of blank computer paper Staple the front page and put your name on it DO NOT GO AHEAD. Stapler is going around. Wait for further directions. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

Introduction of Inductive Reasoning Inductive reasoning can be used to make predictions about the future based on the past or to make conjectures about the past based on the present. Inductive reasoning does not always lead to the truth. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

Inductive Reasoning – Page 1 The process of REASONING that a RULE or statement is TRUE because SPECIFIC AREAS are true Used to form CONJECTURES and to continue patterns, or test hypotheses Conjecture – is a generalized conclusion (not necessarily correct) Taking something specific to something general 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

Steps of Inductive Reasoning Look for a pattern Make a Conjecture Prove the Conjecture or provide a counterexample 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Example 1 Make a conjecture about these next two terms: 7, 14, 21, 28, … 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Example 2 The product of an even number and an odd number is ______________. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Example 3 A scientist takes a piece of salt, turns it over a Bunsen burner, and observes that it burns with a yellow flame. She does this with many other pieces of salt, finding they all burn with a yellow flame. What is the conjecture? 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Your Turn Write an example of a conjecture about two even numbers and prove it. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

Example 4 For the statement, “Every integer of n, n3 is positive” provide a counterexample. To provide if it is false, start plugging in numbers. Let n = 1. Since n3 = 1 and 1 > 0, the conjecture holds. Let n = –2. Since n3 = –8 and –8 < 0, the conjecture false. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Example 5 For the statement, “For any real number x, x2 ≥ x.” provide a counterexample. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Your Turn For the statement, “Two supplementary angles are not congruent.” provide a counterexample. 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning

2-1: Logic with Inductive Reasoning Assignment Page 77 8, 10-13 all, 16, 20-23, 25, 28, 31, 37, 38 4/4/2019 4:54 PM 2-1: Logic with Inductive Reasoning