5. For the following directed graph, let E = {I,J,K,L, M} and let V = {a, b, c,d}. %3D a J L 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. a. If x is an edge, then f (x) is the vertex that the edge points to. b. If x is a vertex, then f (x) is the edge that points to it. c. If x is a vertex, then f (x) is the indegree of x.
5. For the following directed graph, let E = {I,J,K,L, M} and let V = {a, b, c,d}. %3D a J L 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. a. If x is an edge, then f (x) is the vertex that the edge points to. b. If x is a vertex, then f (x) is the edge that points to it. c. If x is a vertex, then f (x) is the indegree of x.
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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IMPORTANT Read all of this please:
PLEASE JUST STATE IF IT IS A FUNCTION OR NOT A FUNCTION for all Parts A, B, C, D, E
If it is, state the domain and codomain in the form "f: X ---> Y"
no explanation and nothing else needed
Transcribed Image Text:5.
For the following directed graph, let E = {I,J,K,L, M} and let V = {a,b, c, d}.
a
d
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.
a. If x is an edge, then f (x) is the vertex that the edge points to.
b. If x is a vertex, then f (x) is the edge that points to it.
c. If x is a vertex, then f (x) is the indegree of x.
d. If x is a natural number, then f (x) is the vertex whose outdegree is x.
e. If x is a subset of V of cardinality 2, then f (x) is the edge connecting the two
vertices in x.
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