Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 18H / c / Solution

False. On the two-state space, takeEvery positive entry of $P$ remains positive in $Q$. Under $P$, both singleton states are closed communicating classes, so neither state is a transient state. Under $Q$, however, state one eventually moves to the absorbing state two and can never return after doing so. State one is therefore transient.