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Prove the following statement directly from the definitions. The product of any two even integers is a multiple of 4. vr such that m =---Select--- v, and there exists ---Select-- Proof: Let m and n be any two even integers. By definition of even there exists ---Select--- such that n = ---Select- v By substitution, mn = 4 - which is an integer because --Select--- v of integers are integers. Thus mn = 4- (an integer), and so 4|mn by definition of divisibility.

Prove the following statement directly from the definitions. The product of any two even integers is a multiple of 4. vr such that m =---Select--- v, and there exists ---Select-- Proof: Let m and n be any two even integers. By definition of even there exists ---Select--- such that n = ---Select- v By substitution, mn = 4 - which is an integer because --Select--- v of integers are integers. Thus mn = 4- (an integer), and so 4|mn by definition of divisibility.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 13E
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Prove the following statement directly from the definitions. The product of any two even integers is a multiple of 4. vs Proof: Let m and n be any two even integers. By definition of even there exists ---Select-- such that n = ---Select--- v v r such that m = ---Select--- v, and there exists --Select--- By substitution, mn = 4 which is an integer because ---Select--- v of integers are integers. Thus mn = 4 (an integer), and so 4|mn by definition of divisibility.
Transcribed Image Text:Prove the following statement directly from the definitions. The product of any two even integers is a multiple of 4. vs Proof: Let m and n be any two even integers. By definition of even there exists ---Select-- such that n = ---Select--- v v r such that m = ---Select--- v, and there exists --Select--- By substitution, mn = 4 which is an integer because ---Select--- v of integers are integers. Thus mn = 4 (an integer), and so 4|mn by definition of divisibility.
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