Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 8H / b / Solution

Reading the directed edges with positive transition probability, the communicating classes areState $3$ can move to $2$ or $4$, and state $4$ can move to $2$ or $5$, so their singleton classes are not closed. Every transition from $1,2,5,$ or $6$ remains within $\{1,2,5,6\}$, so