For each of the following, write TRUE if the statement is always true. Otherwise, write FALSE. No needto show solutions/proofs.(a) If a E An, then (a) < A,.(b) The element 9 is a generator for Z57.(c) In a finite group G, there exists an element of order d if and only if d divides |G|.(d) A cyclic group of order n has no proper nontrivial subgroup if and only if n is prime.(e) If o e Sn such that o = T1 T2 · · Tk where each T; for i = 1, 2, ..., k is a transposition, then for anypositive integer n, o" = Tf'r" - . - T.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For each of the following, write TRUE if the statement is always true. Otherwise, write FALSE. No need to show solutions/proofs. (a) If a € An, then (a) < An- (b) The element 9 is a generator for Z57. (c) In a finite group G, there exists an element of order d if and only if d divides |G|.