Denote by Z, the set of nonnegative integers. Let Rbe the relation on A = R defined by x Ry if x – y is a nonnegative integer, i.e., there exists some n E Z, such that x – y = n. 1. Show that R is a partial order on R. 2. Let B = {2,4} and C = {V2, 4}. Find sup(B). Explain. Does C have an upper bound? Explain. 3. Is Ra total order on R? If yes, explain. If no, given an example why not.

Denote by Z, the set of nonnegative integers. Let Rbe the relation on A = R defined by x Ry if x – y is a nonnegative integer, i.e., there exists some n E Z, such that x – y = n. 1. Show that R is a partial order on R. 2. Let B = {2,4} and C = {V2, 4}. Find sup(B). Explain. Does C have an upper bound? Explain. 3. Is Ra total order on R? If yes, explain. If no, given an example why not.

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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Question

Denote by Z, the set of nonnegative integers.
Let Rbe the relation on A = R defined by x Ry if x – y is a nonnegative integer, i.e., there exists some n E Z, such that x – y = n.
1. Show that R is a partial order on R.
2. Let B = {2,4} and C = {V2, 4}. Find sup(B). Explain. Does C have an upper bound? Explain.
3. Is Ra total order on R? If yes, explain. If no, given an example why not.

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