Decide whether each of the following statements are true.(a) If a, b, m, n ¤ N and a | m and b | n, then ab | mn.(b) If a, b, m, n = N and ab | mn, then either a | m or b|n.[Justify your answers.]

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Answered: Decide whether each of the following…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 4TFE: Label each of the following statement as either true or false. only if

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Question

Decide whether each of the following statements are true.
(a) If a, b, m, n ¤ N and a | m and b | n, then ab | mn.
(b) If a, b, m, n = N and ab | mn, then either a | m or b|n.
[Justify your answers.]

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Decide whether each of the following statements are true. (a) If a, b, m, n E N and am and b | n, then ab | mn. (b) If a, b, m, n = N and ab | mn, then either a | m or b|n.