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Unformatted text preview: Math 100 Expressing Deduction Martin H. Weissman With the language of sets and numbers, one can express many interesting mathematical facts. We have also learned how to use boolean operators (AND, OR, XOR, and NOT) to combine sentences into compound sentences. But to do mathematics, one needs some more connective tissue to express a deductive relationship. The most basic example of this is the If... then... sentence structure. 1. Basic and compound deduction Many facts in basic algebra are most conveniently expressed using an If...then... statement. Consider these examples: If 2 x + 3 = 5, then x = 1. If x is a real number, then x 2 is non-negative. If x is an even number, then y such that 2 y = x . If | x- 3 | = 2, then ( x = 5 or x = 1). Try to complete the following to make a true If...then... sentence: (1) If..., then x > 1. (2) If..., then x = 1 or x =- 1. (3) If x is an even prime number, then... (4) If x 2 = x , then... The If...then... statement is the most basic expression of deduction . It involves a single step of deduction one sentence follows deductively from another. We will discuss methods of deduction later for now, we are focusing only on the language of deduction. More often than not, mathematics involves a compound deduction. One sentence deductively follows another, which follows another, etc... Here are some templates for multi-step deductions: (1) If 2 x + 3 = 5, then 2 x = 2. It follows that x = 1....
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This note was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.
- Fall '08