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Geometry: Section 2.2 Inductive & Deductive Reasoning What you will learn: 1. Use inductive reasoning 2. Use deductive reasoning A conjecture is an unproven statement based on observations. In science this is called a _____________ hypothesis Example: Make a conjecture about the product of an even integer and any other integer. The product of an even integer and any other integer is even. You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case. 46,57 25,36 8 2 n 1 32 32 16 To show a conjecture is true, you must show that it is true for all cases. To show that a conjecture is false, you simply need to show one case where the conjecture is false. A counter example is a specific case for which the conjecture is false Example: Show the conjecture is FALSE by finding a counterexample. a) All prime numbers are odd. 2 is even and a prime number b) The sum of 2 numbers is always greater the larger number. 20 2 or - 3 5 2 Deductive reasoning uses facts, definitions, accepted properties and the laws of logic to form a logical argument. Laws of Logic: Law of Detachment: If the hypothesis of a true conditional statement is true, then the conclusion is also true. Law of Syllogism: If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If these statements are true If hypothesis p, then conclusion r. This statement is true Example: Use the Law of Detachment to make a conclusion from these two statements: If a figure is a square, then it is a rectangle. Quadrilateral ABCD is a square Quad ABCD is a rectangle If it is rainig today, then you can go to the mall. No conclusion possible. Deductive reasoning Inductive reasoning HW: pp80 – 82 / 2-8 Even, 14-24 Even, 30-34 Even, 44