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MY NOTES ASK YOUR TEACH Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms ofrand n can be expressed in terms of s a follows. m = n = Write m - n in terms of r and s and factor out a 2 to obtain m - n = Now is an integer because--Select-- v of integers are integers. Therefore, m - n = 2 · (an integer), and so m – n is -Select-- v by definition of -Select-- v

MY NOTES ASK YOUR TEACH Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms ofrand n can be expressed in terms of s a follows. m = n = Write m - n in terms of r and s and factor out a 2 to obtain m - n = Now is an integer because--Select-- v of integers are integers. Therefore, m - n = 2 · (an integer), and so m – n is -Select-- v by definition of -Select-- v

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...
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MY NOTES ASK YOUR TEACHER Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms ofr and n can be expressed in terms of s as follows. m = n = Write m -n in terms of r and s and factor out a 2 to obtain m -n = Now is an integer because-Select--- v of integers are integers. Therefore, m - n = 2· (an integer), and so m - n is ---Select--- v by definition of --Select--- v.
Transcribed Image Text:MY NOTES ASK YOUR TEACHER Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms ofr and n can be expressed in terms of s as follows. m = n = Write m -n in terms of r and s and factor out a 2 to obtain m -n = Now is an integer because-Select--- v of integers are integers. Therefore, m - n = 2· (an integer), and so m - n is ---Select--- v by definition of --Select--- v.
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