Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x S such that: (a) R1 and R2 are partial orders but R1 U R2 is not. (b) Rị and R2 are equivalence relations but R1U R2 is not. (c) R1 and R2 are partial orders and R1 n R2 is an equivalence relation. (d) each R; is not reflexive, not symmetric, but transitive, while R1U R2 = S x S.

Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x S such that: (a) R1 and R2 are partial orders but R1 U R2 is not. (b) Rị and R2 are equivalence relations but R1U R2 is not. (c) R1 and R2 are partial orders and R1 n R2 is an equivalence relation. (d) each R; is not reflexive, not symmetric, but transitive, while R1U R2 = S x 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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