this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the set consisting of these digits. a) Write down |X|, and find |P(X)|. b) Let Y = {1, 2, 3, 4, 10, 11}. List all the elements of the set X\ Y. c) Let Z = {0, 1, 2, 3, 4, 5}. Define the function f : X → Z by f(x) = x² mod 6 where, as usual, a mod n denotes the remainder upon division of the integer a by the atural number n). (i) Find the image f(X). (ii) State whether f is injective and/or surjective. Does ƒ have an inverse?

this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the set consisting of these digits. a) Write down |X|, and find |P(X)|. b) Let Y = {1, 2, 3, 4, 10, 11}. List all the elements of the set X\ Y. c) Let Z = {0, 1, 2, 3, 4, 5}. Define the function f : X → Z by f(x) = x² mod 6 where, as usual, a mod n denotes the remainder upon division of the integer a by the atural number n). (i) Find the image f(X). (ii) State whether f is injective and/or surjective. Does ƒ have an inverse?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

See similar textbooks