Question: Abstract Algebra Prove #1 (c) using quantified statements. Show ALL steps and give a long proof (Start steps with Let... or Suppose...) 1. Let us

Abstract Algebra

Prove #1 (c) using quantified statements. Show ALL steps and give a long proof (Start steps with "Let..." or "Suppose...")

1. Let us consider (5Z, +) (the set of all multiples of 5 with usual addi- tion).(c) Show that (5Z, +) is cyclic, that is, an element a in 5Z generates (5Z, +), that is, Ha E 5Z, 5Z = {a" [ kez}, that is, . Ly = z 'Z 3 YE 'ZS = ZA 'ZS = DE

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