I have set $A=\{1, 2, 3\}$. $M$ is set of all relations on $A$.
$t:M \to M$ is function that returns the transitive closure for each $R \in M$.
I need to decide if the function $t$ is injective and/or surjective and prove it. the question is how should I do it. I don't even know where to begin because all examples I saw before was for functions like $f(x) = 2x + 3$, etc...
Thank you.