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4. a) Define the following terms: i) POSETS ii) Equivalence relation

4. a) Define the following terms: i) POSETS ii) Equivalence relation

Elements Of Modern Algebra
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...
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OB/s 26% 4:47 PM Edit 88 25 4. a) Define the following terms: i) POSETS ii) Equivalence relation b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows; For every (x, y ) €A, xRy + 5 divides (x2 – y?) and -..3/5 xSy y- 1 = x i) List all the ordered pairs (x, y) in the relation R and S. ii) Ro S iii) SOR (The composite relation R followed by S) c) The Hasse diagram below represents the partial order R on the set X= {1, 2, 3, 4, 5} 3 i) List all the ordered pairs (a, b) such that aRb, for all a,beX ii) Find the maximal and minimal elements 5. а) Define the following with an example: i) Domain of a function ii) One – to - one function 4x +1 A function f is defined on the det of real numbers by f(x) =- 2.x-3 b) i) Write down the domain of f. ii) Show that fis a one – to – one function. iii) Find the inverse of the function f. c) Given the function (x) = x², g(x) = 3x – 4, find the composite W DO Tools Mobile View Share PDF to DOC
Transcribed Image Text:OB/s 26% 4:47 PM Edit 88 25 4. a) Define the following terms: i) POSETS ii) Equivalence relation b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows; For every (x, y ) €A, xRy + 5 divides (x2 – y?) and -..3/5 xSy y- 1 = x i) List all the ordered pairs (x, y) in the relation R and S. ii) Ro S iii) SOR (The composite relation R followed by S) c) The Hasse diagram below represents the partial order R on the set X= {1, 2, 3, 4, 5} 3 i) List all the ordered pairs (a, b) such that aRb, for all a,beX ii) Find the maximal and minimal elements 5. а) Define the following with an example: i) Domain of a function ii) One – to - one function 4x +1 A function f is defined on the det of real numbers by f(x) =- 2.x-3 b) i) Write down the domain of f. ii) Show that fis a one – to – one function. iii) Find the inverse of the function f. c) Given the function (x) = x², g(x) = 3x – 4, find the composite W DO Tools Mobile View Share PDF to DOC
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