Prove that the mapping is order preserving

Question

$ P=Q=\{ \mathcal{P}(S); \subseteq \} $ and $\phi$ from $P \rightarrow Q$ is defined by $\\ \phi (U)= \left\{ \begin{array}{ll} \{1\} & \text{if} \; 1 \in U \\ \{2\} & \text{if} \; 2\in U, \; 1 \notin U\\ \emptyset & \text{otherwise} \\ \end{array} \right. $

Answer 1

It's not order preserving, since $\{2\}\subseteq\{1,2\}$, but $\phi(\{2\})=\{2\}\nsubseteq\{1\}=\phi(\{1,2\}).$