Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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MAT102S - Introduction to Mathematical Proofs - Spring 2010 - UTM Problem Set D - NOT to be submitted. Quiz #2, to be written on Wednesday, February 3rd, from 10:15am to 10:45am at CC1080, will be based on this Problem Set. Work on the following exercises: ± Prove that if x;y are elements of a ±eld, and x ² y = 0 then either x = 0 or y = 0 . Write a detailed solution, and mention which of the ±eld axioms you are using. ± Let F be a ±eld in which 1 + 1 = 0 . Prove that for any x 2 F , x = ³ x . Use only the ±eld axioms and/or claims proved in lecture. Justify each step in your solution.
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Unformatted text preview: FYI: There are many ±elds in which 1 + 1 = 0 . Some of them have in±nitely many elements. ± Chapter 2, Exercises 2.2, 2.3, 2.4, 2.21, 2.28, 2.34(a), 2.38, 2.48. Note : For 2.4 and 2.21, you don’t have to use the logical symbols. You can use words. Also, don’t use the word ‘not’ (or expressions like ‘it is false that’) when you negate a statement. You can, however, use the symbols 6 = and 62 . No explanation is needed for 2.4. In all other questions, you need to justify your answer shortly....
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This document was uploaded on 03/25/2011.

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