Answered: Assume that [a],[b]=( Z12,,5), o([a]) =…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 60RE

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Question

Assume that [a],[b] is an element of (Z₁₂ ,circle plus), order of ([a])=m, order of ([b])=n. Find examples of [a] and [b] (one example for each case, so three examples) for which order of ([a] circle plus [b])=mn, order of ([a] circle plus [b])=lcm(m,n) doesnt equal mn, and order of ([a] circle plus [b]) doesnt equal mn and order of ([a] circle plus [b]) doesnt equal lcm(m,n)

Assume that [a],[b]=(Z,2 ,+), o([a]) = m, o([b]) = n.
Find examples of [a] and [b] (one example for each case, so three examples) for which
o([a]s[b]) = mn, o([a]e[b]) = Icm(m,n) + mn, and o([a]=[b]) + mn and o([a]e[b]) + Icm(m,n)

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