Let us have relations R$1$ from set A to set B$,$ and R$2$ from set B to set C$,$ and R$3=$ R$1$ R$2.$ Which of the following properties hold true?

Here R$3$ is the composition of the sets R$1,$ R$2.$

For every $($a$,$ b$)$ in R$1$ and $($b$,$ c$)$ in R$2,($a$,$ c$)$ is in R$3$

R$3$ is transitive.

R$1$ R$2=$ R$2$ R$1$

For a relation R$4$ from set C to set D$,$ we have:

$($R$1$ R$2)$ R$4=$ R$1($R$2$ R$4)$