2.3 Using Deductive Reasoning to Verify Conjectures

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Sec.2-3 Deductive Reasoning

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2.3 Using Deductive Reasoning to Verify Conjectures Geometry

Reminders Statement _________ statement ______________ ______________ (iff) Symbols p → q q → p ~p → ~q ~q → ~p p ↔ q

Ex 1: Given: p – it is 5th period q – it is time for lunch Write p→q. Write ~p. Write p↔q. Is p↔q true?

Laws of Deductive Reasoning 1. Law of _______________ 2. Law of Syllogism

Law of Detachment If a statement p→q is ________ and a ________ statement p is given, then a third statement q _____________. Given: p→q p q Ex2): 1. If x is even, then x2 is even. 2. x = 6 What statement follows?

Ex.3 & 4 Given: 1. If it is raining, then the ground is wet. 2. It is raining. What follows? Given: 1. If an < is between 0o and 90o, then it is acute. 2. <B is acute. What follows?

Law of Syllogism If p→q is _________ and q→r is ________, then p→r _____________. Given: p→q q→r p→r

Ex 4: Given: 1. If Tony is sick on Friday, then he cannot play football. 2. If Tony cannot play football, then the team will lose. What statement follows? q p→q q→r p→r p r

Ex 5: Given: p→q q→s r→s r→q What follows? . Given: q→r s→t r→s p→q

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