How to proof that a specially defined Transitive Join for the relations $R \subseteq A\times B$ und $S \subseteq B\times C$ is associative?
The join is defined as: $R \Join S =\_\text{def} \{(a,c)\mid \text{there is a } b \in B \text{ with } (a,b) \in R \text{ and }(b,c) \in S\}. $ My question is how do you proof that $\Join$ is associative meaning that $(R \Join S) \Join T = R \Join (S \Join T)$ for $R\subseteq A\times B, S \subseteq B\times C $ and $ T \subseteq C \times D$ holds