MATH135_W12_Assignment_2_Solns

# MATH135_W12_Assignment_2_Solns - 1 MATH 135 W 2012...

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1 MATH 135 W 2012: Assignment 2 Due: 8:30 AM, Wed., 2012 Feb. 1 in the dropboxes outside MC 4066 Write your answers in the space provided. If you wish to typeset your solutions, use the solution template posted on the course web site. Typesetting is done in L A T E X. A very good online all purpose L A T E Xmanual is the L A T E Xwikibook at http://en.wikibooks.org/wiki/LaTeX . Links to installations for various operating systems are also included there. Stephen Carr is IST’s L A T E Xgoto person, and his introductory guide is at http://www.ist.uwaterloo.ca/ew/saw/latex/latex_getstarted.pdf . Family Name: First Name: I.D. Number: Section: Mark: (For the marker only.) If you used any references beyond the course text and lectures (such as other texts, discussions with colleagues or online resources), indicate this information in the space below. If you did not use any aids, state this in the space provided. 1. Consider the following statement: Statement 1. Suppose a is an integer. If 32 - (( a 2 + 3)( a 2 + 7)) , then a is even. In trying to prove or disprove this statement, each of parts (a), (b) and (c) contains a ﬂaw. Determine the main ﬂaw in each argument. (a) Suppose a is even. Then a 2 is even, so both a 2 + 3 and a 2 + 7 are odd. Since 32 is even, 32 - (( a 2 + 3)( a 2 + 7)). Solution. The ﬁrst sentence assumes that the conclusion is true.

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2 (b) Let a = 1. Then 32 | (( a 2 + 3)( a 2 + 7)), but a is not even. This is a counterexample to the statement. Solution.
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MATH135_W12_Assignment_2_Solns - 1 MATH 135 W 2012...

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