PLEASE ANSWER ALL PARTS OF THIS QUESTION.For the following directed graph, let ? = {?,?,?, ?, ?} and let ? = {?, ?, ?, ?}.For the definition of ? below, determine if ? is a function. If it is a function, state its domain and codomain in the form “?:? → ?” and give a table of values that lists each element ? of the domain along with the corresponding element ��(?) of the codomain. If the given ? is not a function, explain why not.If ? is a natural number, then ?(?) is the vertex whose outdegree is ?. ## Problem 5: Directed Graph and Function AnalysisConsider the following directed graph with:- Edges \(E = \{I, J, K, L, M\}\)- Vertices \(V = \{a, b, c, d\}\)### Graph DescriptionThe graph consists of directed edges between the vertices:- Edge \(I\) goes from vertex \(a\) to \(d\).- Edge \(J\) goes from vertex \(a\) to \(b\).- Edge \(K\) goes from vertex \(b\) to \(c\).- Edge \(L\) goes from vertex \(d\) to \(c\).- Edge \(M\) goes from vertex \(a\) to \(c\).### TaskFor each definition of the function \(f\) below, determine the following:1. If \(f\) is a function.2. If it is a function, provide: - The domain and codomain in the form \(f: X \rightarrow Y\). - A table listing each element \(x\) of the domain with the corresponding \(f(x)\) in the codomain.3. If the given \(f\) is not a function, explain why.### DefinitionFor part \(d\):- \(f(x)\) is defined such that if \(x\) is a natural number, then \(f(x)\) is the vertex whose outdegree is \(x\).### Analysis- **Outdegree of each vertex:** - Vertex \(a\): 3 (edges \(I, J, M\)) - Vertex \(b\): 1 (edge \(K\)) - Vertex \(c\): 0 - Vertex \(d\): 1 (edge \(L\))Given this definition of \(f(x)\), analyze whether \(f\) is indeed a function based on the uniqueness of this mapping for each natural number \(x\).

Answered: Image /qna-images/answer/1d4f49c1-c4ea-4dd8-8879-bcdd00e0218d.jpg

For the following directed graph, let E = {I,J, K,L, M} and let V = {a,b, c, d}. a J M b K For each definition of f below, determine if f is a function. If it is a function, state its domain and codomain in the form "f:X → Y" and give a table of values that lists each element x of the domain along with the corresponding element f (x) of the codomain. If the given f is not a function, explain why not.

For the following directed graph, let E = {I,J, K,L, M} and let V = {a,b, c, d}. a J M b K For each definition of f below, determine if f is a function. If it is a function, state its domain and codomain in the form "f:X → Y" and give a table of values that lists each element x of the domain along with the corresponding element f (x) of the codomain. If the given f is not a function, explain 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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PLEASE ANSWER ALL PARTS OF THIS QUESTION. For the following directed graph, let ? = {?,?,?, ?, ?} and let ? = {?, ?, ?, ?}. For the definition of ? below, determine if ? is a function. If it is a function, state its domain and codomain in the form “?:? → ?” and give a table of values that lists each element ? of the domain along with the corresponding element ?(?) of the codomain. If the given ? is not a function, explain why not. If ? is an edge, then ?(?) is the vertex that the edge points to.