Are These Relations Reflexive, Antisymmetric, and Transitive?

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Homework Help Overview

The discussion revolves around determining the properties of two mathematical relations, specifically whether they are reflexive, antisymmetric, and transitive. The relations are defined in terms of inequalities involving pairs of variables.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the properties of the relations, with one original poster attempting to classify each relation based on the definitions of reflexivity, antisymmetry, and transitivity. Questions arise regarding the reflexivity of the second relation, particularly after a clarification about a potential typo in its definition.

Discussion Status

The discussion is ongoing, with participants questioning the implications of the corrected definition of the second relation. Some guidance has been provided regarding the classification of the relations, but there is no explicit consensus on all aspects yet.

Contextual Notes

There is a noted typo in the definition of the second relation that may affect its classification, and participants are actively considering how this impacts their evaluations of reflexivity, antisymmetry, and transitivity.

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Homework Statement


Are these two relations reflexive, antisymmetric, transitive?

1. (w,x)<=(y,z) iff w+x <= y+z

2. (w,x)<=(y,z) iff w+x <= y+z AND w<y

Homework Equations





The Attempt at a Solution



1. reflexive - yes; antisymmetric - no; transitive - yes;

2. reflexive - yes; antisymmetric - yes; transitive - yes;
 
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would you say the second is reflexive?
 
lanedance said:
would you say the second is reflexive?

With the way I wrote it no. But I actually made a typo, it should be w+x <= y+z AND w<=y. So I'd say yes
 
ok, would that change anything else?
 
lanedance said:
ok, would that change anything else?

No, I think #2 would still be antisymmetric and transitive
 

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