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