Let's say we have set: $A = \{1,2,3,...,10\}$, and there is a relation $M=P(A)-{\phi}=\{X | X\subseteq A, x\neq \phi\}.$
And there is this relation:
- $T$ is defined as: $\{X,Y\}\in T$ iff $\{X,Y\}$ is a partition of $A$.
So to find out whether it's transitive, I first tried to find the result of the relation $M$, and then found it to be almost impossible and impractical, as calculating $2^{10}$ of subsets is not the best idea, and the by using this I could calculate the $R^2$, but that's not the case this time.
Then I tried finding whether it's Symmetric, but because I couldn't calculate $M$, as I think I can't also find $M^{-1}$.
And.. I am pretty sure it's not reflexive as it can't have the Identity because it's the $P(A)$ of this set, meaning there isn't a set like this one: $\{1,1\}$.
I would like to get some assistance \ explanation on finding whether a relation is reflexive, symmetric, and transitive.