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b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (x, y ) еА, xRy 9 5 divides (x² – y?) and xSy y-1 =x i) List all the ordered pairs (x, y) in the relation R and S. ii) Ros ii) SOR (The composite relation R followed by S)

b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (x, y ) еА, xRy 9 5 divides (x² – y?) and xSy y-1 =x i) List all the ordered pairs (x, y) in the relation R and S. ii) Ros ii) SOR (The composite relation R followed by S)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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OB/s S .l 4 O 40% 5:41 PM Edit 88 25 b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (х, у ) €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) RnS 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} 4 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 b) A functionf is defined on the det of real numbers by f(x) = 2x -3 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 f(x) = x?, g(x) = 3x – 4, find the composite function gof (where gof'means f'followed by g) d) A function / is defined on the set N of natural numbers by 88 W DO Tools Mobile View Share PDF to DOC
Transcribed Image Text:OB/s S .l 4 O 40% 5:41 PM Edit 88 25 b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (х, у ) €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) RnS 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} 4 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 b) A functionf is defined on the det of real numbers by f(x) = 2x -3 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 f(x) = x?, g(x) = 3x – 4, find the composite function gof (where gof'means f'followed by g) d) A function / is defined on the set N of natural numbers by 88 W DO Tools Mobile View Share PDF to DOC
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