Prove that $\text{Domain}(S\circ R) \subset \text{Domain}(R)$ where $ R $ is a relation from $ A $ to $ B $ and $ S $ is a relation from $ B$ to $ C $.
My solution: I suppose that there is an element $a$ which is a an element of the domain of $S$ composition $R$. Then there is an element $b$ which is an element of $B$ such that $(a,b)$ is an element of $R$ and $(b,c)$ is an element of $S$. Hence $a$ is an element of the domain of $R$. Hence Proven.