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For the following directed graph, let E = {I,J,K,L,M} and let V = {a,b, c, d}. %3D a d 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 eac element x of the domain along with the corresponding element f(x) of the codomai 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}. %3D a d 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 eac element x of the domain along with the corresponding element f(x) of the codomai If the given f is not a function, explain why not.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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*Discrete math

 

Please answer part C of this question with clear steps. Thank you!

**c.** If \( x \) is a vertex, then \( f(x) \) is the indegree of \( x \). Explanation: This statement is discussing a concept from graph theory. In a directed graph, each vertex can have edges directed towards it, known as the indegree. The function \( f(x) \) maps the vertex \( x \) to its indegree, providing a numerical representation of how many incoming edges are connected to that vertex. There are no graphs or diagrams to explain in this image.
Transcribed Image Text:**c.** If \( x \) is a vertex, then \( f(x) \) is the indegree of \( x \). Explanation: This statement is discussing a concept from graph theory. In a directed graph, each vertex can have edges directed towards it, known as the indegree. The function \( f(x) \) maps the vertex \( x \) to its indegree, providing a numerical representation of how many incoming edges are connected to that vertex. There are no graphs or diagrams to explain in this image.
For the following directed graph, let \( E = \{ I, J, K, L, M \} \) and let \( V = \{ a, b, c, d \} \). The diagram shows a directed graph with the following nodes and edges: - Node \( J \) has an arrow pointing to node \( I \). - Node \( I \) has an arrow pointing to node \( M \). - Node \( M \) has an arrow pointing to node \( L \). - Node \( L \) has an arrow pointing to node \( d \). - Node \( b \) has an arrow pointing to node \( K \). - Node \( K \) has an arrow pointing back to node \( c \). 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 “\( f: X \rightarrow Y \)” 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.
Transcribed Image Text:For the following directed graph, let \( E = \{ I, J, K, L, M \} \) and let \( V = \{ a, b, c, d \} \). The diagram shows a directed graph with the following nodes and edges: - Node \( J \) has an arrow pointing to node \( I \). - Node \( I \) has an arrow pointing to node \( M \). - Node \( M \) has an arrow pointing to node \( L \). - Node \( L \) has an arrow pointing to node \( d \). - Node \( b \) has an arrow pointing to node \( K \). - Node \( K \) has an arrow pointing back to node \( c \). 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 “\( f: X \rightarrow Y \)” 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.
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