OB/s S.l 4 O 40% 5:41 PMEdit8825b)Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on Aas follows:For every (х, у ) €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)RnSiii)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}43i)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+1b)A functionf is defined on the det of real numbers by f(x) =2x -3i)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 compositefunction gof (where gof'means f'followed by g)d)A function / is defined on the set N of natural numbers by88WDOToolsMobile ViewSharePDF to DOC

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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)

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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For the set A = {are, bot, cab, era}, define the relation R on A to be: (x,y) e R if and only if word x and word y share one letter only. For example (are, cab) is in R because those words share one letter only ("a"). But (are, era) is NOT in R because those words do NOT share one letter only, they share 3 letters. Also (bot, era) is NOT in R since they share no letters at all. In cach part, answer yes or no. If yes, then explain why in terms of this specific relation about sharing letters (not just by stating the generic definition of the property). If you say a) Is R reflexive? b) Is R symmetric? c) Is R antisymmetric? d) Is R transitive?
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Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 = %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is, x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.
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3. а) Define the following terms as used in graph theory: i) regular graph ii) simple circuit [1 1 2] Let A =|1 0 1 be the adjacency matrix for the graph G, with 2 1 0 b) vertices vi, v2, v3. i) Find the number of walks of length 2, from vị to vị. ii) Draw the graph G and label the edges e, (i = 1, 2, 3. ...) iii) Write down the walks of length 2 from vị to vị. Which ones are simple circuits? [1 1 1 01 0 10 0 0 0 1 1 li 0 0 1 c) The matrix M = |8 : represents the relations R defined om the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. ii) Draw the graph representing the relation R. How many edges does a 50-regular granh with 100 vertices bave2
Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (x, y ) eA, 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) RnS iii) SoR (The composite relation R followed by S)
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Let P={1.2,3,4,12,36} and the relation set R={(1,1) ,(2,2),(3,3),(4,4),(12,12),(36,36),(1,2),(1,3),(1,4),(1,12),(1,36),(2,4)(2,12),(2,36),(3,12),(3,26),(4,12),(4,36)}. Show that (P,R) is a poser. Represent the relation using the diagraph and then draw the Hasse diagram.