1*) Let X = {1,2, 3}, Y = {2,3, 4}, and Z = {1,2}.(a) Define a function f: Z → X that is one-to-one but not onto.(b) Define a function g: X → Z that is onto but not one-to-one.(c) State whether there exists a function h: X →Y that is one-to-one but not onto.

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Answered: 1*) Let X = {1,2, 3}, Y = {2,3, 4}, and…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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1*) Let X = {1,2, 3}, Y = {2,3, 4}, and Z = {1,2}. (a) Define a function f: Z → X that is one-to-one but not onto. (b) Define a function g: X → Z that is onto but not one-to-one. (c) State whether there exists a function h: X →Y that is one-to-one but not onto.