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Let R ⊆ A × A be a a binary relationship defined in a non-empty set A. Let B be any set so that B⊆ A. Define the set Rb as RB := R ∩ (B × B).  1.) How to show that if R is reflexive, symmetric and transitive then Rb also is.  2.) Is the opposite true? Demonstrate truth or falseness.  3.) If R is antisimetric, is Rb antisimetric too?

Let R ⊆ A × A be a a binary relationship defined in a non-empty set A. Let B be any set so that B⊆ A. Define the set Rb as RB := R ∩ (B × B).  1.) How to show that if R is reflexive, symmetric and transitive then Rb also is.  2.) Is the opposite true? Demonstrate truth or falseness.  3.) If R is antisimetric, is Rb antisimetric too?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Let R ⊆ A × A be a a binary relationship defined in a non-empty set A. Let B be any set so that B⊆ A. Define the set Rb as RB := R ∩ (B × B). 

1.) How to show that if R is reflexive, symmetric and transitive then Rb also is. 

2.) Is the opposite true? Demonstrate truth or falseness. 

3.) If R is antisimetric, is Rb antisimetric too? 

 

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I'm having a bit of trouble understanding on question 2 how R is not symmetric, as each pair has its inverse in the Relationship as well( (1,1), (2,2), (3,3) are symmetric by nature and (2,1) is the symmetry of (1,2) ) 

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