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Chapter 7 �Relations:� The Second �Time Around

Reporter: Feng-Hsu Chiang

Student ID: 312706001

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Relations Revisited: Properties of Relations

7.1

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Definition 7.1

 

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Definition 7.2

 

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Example 7.4

 

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Definition 7.3

 

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Example 7.6

 

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Definition 7.4

 

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Example 7.10

 

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Definition 7.5

 

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Example 7.12

 

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Definition 7.6

 

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Example 7.14(a)

 

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Definition 7.7

 

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Example 7.16(b)

 

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Example 7.16(e)

 

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Computer Recognition: Zero-One Matrices and Directed Graphs

7.2

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Definition 7.8

 

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Example 7.17

 

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Theorem 7.1

 

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Definition 7.9

 

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Example 7.19

 

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Definition 7.10

 

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Example 7.20

 

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Example 7.21

 

 

 

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Example 7.21(cont.)

 

 

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Example 7.21 (cont.)

 

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Properties

 

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Definition 7.11

 

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Example 7.23

 

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Definition 7.12

 

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Definition 7.13

 

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Example 7.24

 

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Theorem 7.2

 

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Definition 7.14

 

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Example 7.25

 

isolated vertex

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Example 7.25 (cont.)

 

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Example 7.26

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Example 7.26 (cont.)

 

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Definition 7.15

 

This graph is strongly connected and loop-free.

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Example 7.28

 

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Example 7.28 (cont.)

 

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Example 7.29

 

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Example 7.30

 

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Example 7.31

 

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Example 7.32

 

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Example 7.32 (cont.)

 

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Example 7.33