OB/s26% 4:47 PMEdit88254. a)Define the following terms:i)POSETSii)Equivalence relationb)Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on Aas follows;For every (x, y ) €A,xRy + 5 divides (x2 – y?) and-..3/5xSy y- 1 = xi)List all the ordered pairs (x, y) in the relation R and S.ii)Ro Siii)SOR (The composite relation R followed by S)c)The Hasse diagram below represents the partial order R on theset X= {1, 2, 3, 4, 5}3i)List all the ordered pairs (a, b) such that aRb, for alla,beXii)Find the maximal and minimal elements5. а)Define the following with an example:i)Domain of a functionii)One – to - one function4x +1A function f is defined on the det of real numbers by f(x) =-2.x-3b)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 compositeWDOToolsMobile ViewSharePDF to DOC

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Math

Advanced Math

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

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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Question

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
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