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

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MAT102S - Introduction to Mathematical Proofs - Spring 2010 - UTM Problem Set C - TO BE SUBMITTED TO YOUR TA Due : Monday, January 25, in tutorials. ± This assignment must be submitted to your TA at the beginning of the tutorial on the above date. ± Marking scheme : 8 marks for your solutions to the problems assigned (only some of the questions will be marked) and 2 marks for presentation. ± To receive the 2 marks allotted to presentation, you must submit at least half of the problems assigned and pay attention to the following: { Your full name, student number, tutorial section and the name of your TA appear in the top of the ±rst page. { The section and question number (including a,b,c. .. if the question has several parts) are clearly indicated at the beginning of each of your answers. { Your assignment is stapled in the top left corner (if it is more than one page in length).
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Unformatted text preview: { You are using a clean paper (no ripped paper), that is not folded or rolled. { Your writing is clear and organized (use full sentences), and your reasoning is easy to follow. Submit your solutions to the following problems from the textbook: 1. Chapter 1, Exercises 1.17, 1.35, 1.46(b), 1.49, 1.50 . 2. Is the set R 2 , with addition and multiplication dened below a eld? Explain. ( a;b ) + ( c;d ) = ( a + c;b + d ) ( a;b ) ( c;d ) = ( ac;bd ) 3. Is the set [0 ; 1 ) (with the usual addition and multiplication) a eld? Explain. 4. Let F = f ; 1 ;a;b g be a eld with four elements. Prove that a 2 = b . You may use a result proved during lecture....
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