Discrete Math13. For the following digraphs, determine ISI, the cardinality of S if:a) S is the transitive closure of R?bb) S is the symmetric closure of R.c) S is the reflexive closure of R.

A={a,b,c,d,e} The given relation as R={(b,c), (b,e), (c,e), (e,b), (e,c), (d,a)} For transitive…

Answered: 13. For the following digraphs,…

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 each of the following, determine which of these choices is correct. Let Rj and R be two non-empty relations on a set A. a) Rj and R, are transitive = R,OR, is transitive b) Rj and R2 are symmetric > R¡UR2 is symmetric c) Rj and R2 are transitive = R¡UR, is not transitive d) Rj and R; are reflexive R,NR, is reflexive
State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric, and Transitive. Then construct three small worlds showing, respectively, that a relation can be Reflexive and not Symmetric, Symmetric and not Transitive, and Reflexive and not Transitive. Finally, for each of the three small worlds that you construct, give an example of a relation in ordinary language that works like the relation in the small world you built. That is, for your first small world, give an ordinary language example of a relation that is Reflexive and not Symmetric.
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13. For the following digraphs, determine ISI, the cardinality of S if: a) S is the transitive closure of R? b d b) S is the symmetric closure of R. b d c) S is the reflexive closure of R. d