2. Decide if the statement is True or False. Justify your answer. Explain why is it true orwhy not, and give an example/counterexample where necessary.a) Does the poset (P(Z), ≤) have mimmal element(s)?There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m =|V₂l.c) The sum of all vertex degrees in an undirected graph is always even number.d) Kn has a Hamiltonian circuit for every natural number n ≥ 3.|V₁|, n ==

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Math

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There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m = |V2I. |V₁|,n=

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

2. Decide if the statement is True or False. Justify your answer. Explain why is it true or
why not, and give an example/counterexample where necessary.
a) Does the poset (P(Z), ≤) have mimmal element(s)?
There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m =
|V₂l.
c) The sum of all vertex degrees in an undirected graph is always even number.
d) Kn has a Hamiltonian circuit for every natural number n ≥ 3.
|V₁|, n =
=

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Can you explain the solution a bit more as I am not understanding how you proved it to be false?

Is it false cause degree m+n would imply a vertex in M or N that has edges contained within the subset which breaks definition of bipartite?

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