Let S ⊆ N, and for any x, y ∈ N, consider a relation R such that xRy if and only if there exists z ∈ S such that x + z = y. Show that if R is a partial order, then (a) 0 ∈ S (b) for any x, y ∈ S, x + y ∈ S.

Let S ⊆ N, and for any x, y ∈ N, consider a relation R such that xRy if and only if there exists z ∈ S such that x + z = y. Show that if R is a partial order, then (a) 0 ∈ S (b) for any x, y ∈ S, x + y ∈ 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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