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In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam number. 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 natural number n). (i) Find the image f(X). (ii) State whether f is injective and/or surjective. Does f have an inverse?

In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam number. 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 natural number n). (i) Find the image f(X). (ii) State whether f is injective and/or surjective. Does f have an inverse?

Advanced Engineering Mathematics
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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...9 In this question and subsequently, let d₁, d2, . d5 denote the first five digits of your exam number. 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 natural number n). (i) Find the image ƒ(X). (ii) State whether f is injective and/or surjective. Does f have an inverse?
Transcribed Image Text:...9 In this question and subsequently, let d₁, d2, . d5 denote the first five digits of your exam number. 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 natural number n). (i) Find the image ƒ(X). (ii) State whether f is injective and/or surjective. Does f have an inverse?
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