(b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs only. cRc, aRa, aRb, aRc, bRc, cRb. (i) Draw a digraph representing the relation R. (ii) The relation R is not an equivalence relation. Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become an equivalence relation. (iii) Give the equivalence classes for the equivalence relation from (b)(ii).

(b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs only. cRc, aRa, aRb, aRc, bRc, cRb. (i) Draw a digraph representing the relation R. (ii) The relation R is not an equivalence relation. Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become an equivalence relation. (iii) Give the equivalence classes for the equivalence relation from (b)(ii).

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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Considering A as a set which contains the elements {2,3,4,5,6,7,8}, Define a relation R from A to A by R={(xy): y is multiple of x and x#y} [Multiple means "a number that may be divided by another a certain number of times without a remainder. Example: "15, 20, are multiples of 5" a. Write R b. Depict this relation R using an arrow diagram. c. Write the matrix representation for R. d. Check whether R is reflexive, symmetric, antisymmetric.
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