In deterministic system with states $0,1,2,3$ and $4,$ the transition from state to state are given as follows:

$(00),(04),(10),(20),(43),(13),(32),(33)$

A$)$ Construct the transition graph of the system.

B$)$ Construct the Boolean matric of the transition.

$x=\{\begin{array}{c}[0]\\ 1\\ 1\\ 3\\ 4\end{array}\left[\begin{array}{c}4\\ 10\\ 2\\ 6\\ 1\end{array}\right]$ at time $t.$ find the state $Y$ ate time $t+1.$