Prove that T is a subring of R Let $R$ and $S$ be rings and $h$ and $g$ be homomorphisms from $R$ into $S$. 
Let $T=\{r| r\in R$ and $h(r)=g(r)\}$
Prove that $T$ is a subring of $R$. 
I understand what the question is asking but I am a little confused on how to get it started. I know that I have to prove $T\neq \emptyset$; $rt\in T$ for all $r,t\in T$; and $r-t\in T$ for all $r,t\in T$ right? But I'm not really sure how I can do that. Also, I don't get what $T$ is actually being defined as. I don't want the answer just how to get started and what does $T$ actually mean? Thanks. 

$T$ is just the set of those elements in the domain, $R$, that take the same value when mapped by the homomorphisms $g$ and $h$.
Hope this makes it clearer.
