1. **Problem:** If $A \subseteq B$, prove that $C - B \subseteq C - A$. 2. **Formula and rules:** - Set difference $X - Y = \{x : x \in X \text{ and } x \notin Y\}$. - If $A \subseteq B$, then every element of $A$ is in $B$. 3. **Proof steps:** - Let $x \in C - B$. By definition, $x \in C$ and $x \notin B$. - Since $A \subseteq B$, if $x \notin B$, then $x \notin A$ (because if $x$ were in $A$, it would be in $B$). - Therefore, $x \in C$ and $x \notin A$, so $x \in C - A$. 4. **Conclusion:** Every $x$ in $C - B$ is also in $C - A$, so $C - B \subseteq C - A$. Final answer: $\boxed{C - B \subseteq C - A}$