Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a), (1, 1), (a, 1), (1, a), (3, 1), (1,3), (3, a), (a, 3), (b, b), (b, 2), (2, c)} (a) Draw a digraph representing the relation R. (b) Show that R is not transitive. (c) Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become transitive.

Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a), (1, 1), (a, 1), (1, a), (3, 1), (1,3), (3, a), (a, 3), (b, b), (b, 2), (2, c)} (a) Draw a digraph representing the relation R. (b) Show that R is not transitive. (c) Justifying your answer, find the smallest set of related pairs which must be added to R in order for it to become transitive.

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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