Markov chains — a self-contained pair of states

Suppose $\{X_n,n\ge0\}$ is a Markov chain with state space $S=\{1,2,3,4\}$ and transition probability matrix

$$P=\begin{pmatrix}1/2&0&1/2&0\\0&1/3&0&2/3\\2/3&0&1/3&0\\0&1/4&0&3/4\end{pmatrix}.$$

Which of the following options is true?