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?
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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Transcribed Image Text:...9
In this question and subsequently, let d₁, d2, . d5 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
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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