Question

Consider the directed graph G with vertex set V as diagrammed: Let $R^+$ be the binary relation on V given by $iR^+j$ whenever there is a walk in G from i to j. $R^+$ is an equivalence relation for this graph. What is the partition of V defined by the equivalence relation $R^+$? {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8} {1,5}, {2,6}, {3,7}, {4,8} {1,2,3,4}, {5,6,7,8} {1, 2, 3, 4, 5, 6, 7, 8}

Name: consider the directed graph g with vertex set v as diagrammed let r be the binary relation on v given by irj whenever there is a walk in g from i to j r is an equivalence relation for this g 53183
Uploaded: 2023-04-17T23:31:40-08:00
Duration: 2 min 56 s
Channel: Sri K
Description: consider the directed graph g with vertex set v as diagrammed let r be the binary relation on v given by irj whenever there is a walk in g from i to j r is an equivalence relation for this g 53183

          Consider the directed graph G with vertex set V as diagrammed:

Let $R^+$ be the binary relation on V given by $iR^+j$ whenever there is a walk in G from i to j. $R^+$ is an equivalence relation for this graph.
What is the partition of V defined by the equivalence relation $R^+$?
{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}
{1,5}, {2,6}, {3,7}, {4,8}
{1,2,3,4}, {5,6,7,8}
{1, 2, 3, 4, 5, 6, 7, 8}

consider the directed graph g with vertex set v as diagrammed let r be the binary relation on v given by irj whenever there is a walk in g from i to j r is an equivalence relation for this g 53183

Added by Kelsey L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

04/17/2023

Step 1

Two vertices $i$ and $j$ are in the same equivalence class if there is a walk from $i$ to $j$ and a walk from $j$ to $i$. Show more…

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Consider the directed graph G with vertex set V as diagrammed: Let $R^+$ be the binary relation on V given by $iR^+j$ whenever there is a walk in G from i to j. $R^+$ is an equivalence relation for this graph. What is the partition of V defined by the equivalence relation $R^+$? {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8} {1,5}, {2,6}, {3,7}, {4,8} {1,2,3,4}, {5,6,7,8} {1, 2, 3, 4, 5, 6, 7, 8}