Chapter 2 Deductive Reasoning

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Presentation transcript:

Chapter 2 Deductive Reasoning Proving statements by reasoning from accepted postulates, definitions, theorems, and given information.

2-1 If – then statements; Converses A) Terms 1) If – then statements or conditional statements. Ex. If it is raining, then it is Monday. hypothesis conclusion a) Symbol: p: hypothesis q: conclusion Ex. If p, then q. (p → q)

Ex. Statement: Elephants are grey. Conditional statement: If an animal is an elephant, then it is grey. Ex. Statement: A catfish is a fish that has no scales. If a fish is a catfish, then it has no scales.

2) Converse statements is reversing the hypothesis and conclusion of a conditional statement. a) symbol: If q, then p. (q → p) Ex. Converse: If an animal is grey, then it is an elephant. Ex. Converse: If a fish has no scales, then it is a catfish. *Some converse statements are false based on the conditional statement.

3) Counterexample is an example that proves an if – then statement is false. *It takes only one counterexample to prove something is false. Ex. If Sue lives in Pennsylvania, then she lives in Reading. Counterexample: She could live in Allentown or any other city in Pennsylvania.

B) Different ways an if, then form can be written. 1) If p, then q ex. If x = 3, then 6x = 18 2) p implies q x = 3 implies 6x = 18 3) p only if q x = 3 only if 6x = 18 4) q if p 6x = 18 if x = 3