et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈ S such that a + c = b. Show that if R is a partial order, then (i) 0 ∈ S (ii) for any a, b ∈ S, a + b ∈ S. You do not need to write a formal proof – a clear, concise and correct justification is sufficient.

et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈ S such that a + c = b. Show that if R is a partial order, then (i) 0 ∈ S (ii) for any a, b ∈ S, a + b ∈ S. You do not need to write a formal proof – a clear, concise and correct justification is sufficient.

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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