Fe ench of the fellowing funeticns, determine (i) whether or not it is injecetive and (i) wbether or not it is surjective. (a) f: 2/5- Z/5 defiaed by f(a) - ar. (b) /: Z/6 -- Z/6 defised by f(e) - dr. (e) Let S be the set of all wqunces ( with a. e (0, 1..), and kt /:8- 0.1] be defined by

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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For each of the following functions, determine (i) whether or not it is injective and (ii) whether or not it is subjective.

For ench of the following buncticns, determine (i) whether or not it is injective and (i)
wbether or not it is surjective.
(a) f: Z/5 -- Z/5 defised by f(r) - 3r.
(b) S:Z/6 -- Z/6 defined by f(e) - dr.
(e) Let S be the set of all wequences ( with a. E (0, 1.), and kt fi8- j0, 1]
be defned by
Transcribed Image Text:For ench of the following buncticns, determine (i) whether or not it is injective and (i) wbether or not it is surjective. (a) f: Z/5 -- Z/5 defised by f(r) - 3r. (b) S:Z/6 -- Z/6 defined by f(e) - dr. (e) Let S be the set of all wequences ( with a. E (0, 1.), and kt fi8- j0, 1] be defned by
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