5. True or falsea. Every permutation is a one-to-one functionb. Every function is a permutation iff it is one-to-onec. Every function from a finite set to itself must be one-to-oned. Every element of the group generates a cyclic subgroup of the groupe.The symmetric group S10 has 10 elementsf. Sn is not cyclic for any ng. Every permutation is a cycleh.Every cycle is a permutation

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 42E: 42. For an arbitrary set , the power set was defined in Section by , and addition in was...

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True or false a. Every permutation is a one-to-one function b. Every function is a permutation iff it is one-to-one c. Every function from a finite set to itself must be one-to-one