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, 05:52 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, 06:09 PMThePerfectHacker
Given a set $\displaystyle A$ and a relation $\displaystyle R$ on $\displaystyle A$ a reflexsive property is defined as if $\displaystyle yRx$ then, $\displaystyle xRy$. Now the meaning of $\displaystyle yRx$ is $\displaystyle (y,x)\in R$.

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 $\displaystyle \{1,2,3\}$ - Oct 29th 2006, 06:16 PMhenshilwood
- Oct 29th 2006, 06:48 PMThePerfectHacker
- Oct 30th 2006, 02:56 AMtopsquark
- Oct 30th 2006, 04:03 AMThePerfectHacker
- Oct 30th 2006, 04:55 AMPlato
The relation $\displaystyle \Delta _A = \left\{ {\left( {1,1} \right),\left( {2,2} \right),\left( {3,3} \right)} \right\}$ 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 $\displaystyle 2^6 $ subsets of the off-diagonal pairs. Unite each of those with the diagonal to get a reflexive relation on A. That is, there are $\displaystyle 2^6 $ reflexive relations on A.

- Oct 30th 2006, 08:16 AMThePerfectHacker
- Oct 30th 2006, 08:59 AMPlato
Well, that is certainly not what he wrote.

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