Need help understanding reflexive properties of Abstract algebra. If A = {1, 2, 3} what are its reflexive properties?

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- Oct 29th 2006, 06:52 PMhenshilwoodAbstract Algebra Reflexive Properties
Need help understanding reflexive properties of Abstract algebra. If A = {1, 2, 3} what are its reflexive properties?

- Oct 29th 2006, 07:09 PMThePerfectHacker
Given a set and a relation on a reflexsive property is defined as if then, . Now the meaning of is .

The reflexive property appears in two specific types of relations. An**equivalence relation**used a lot in abstract algebra and**partial ordering relation**a favorite in set theory.

I cannot answer thy question for thee has not defined a relation of - Oct 29th 2006, 07:16 PMhenshilwood
- Oct 29th 2006, 07:48 PMThePerfectHacker
- Oct 30th 2006, 03:56 AMtopsquark
- Oct 30th 2006, 05:03 AMThePerfectHacker
- Oct 30th 2006, 05:55 AMPlato
The relation is called the diagonal relation. Any relation that contains the diagonal is a reflexive relation. Now there are 6 off-diagonal pairs in AxA. Thus, there are subsets of the off-diagonal pairs. Unite each of those with the diagonal to get a reflexive relation on A. That is, there are reflexive relations on A.

- Oct 30th 2006, 09:16 AMThePerfectHacker
- Oct 30th 2006, 09:59 AMPlato
Well, that is certainly not what he wrote.

I took him at his word: “Need help understanding reflexive properties ..”.