1. **State the problem:** We want to find sets $A$, $B$, and $C$ such that: - $A \subseteq B$ (A is a subset of B) - $B \subset C$ (B is a proper subset of C) - $A \not\subset C$ (A is not a subset of C) 2. **Analyze the conditions:** - $A \subseteq B$ means every element of $A$ is in $B$. - $B \subset C$ means every element of $B$ is in $C$, and $B \neq C$. - $A \not\subset C$ means there is at least one element in $A$ that is not in $C$. 3. **Check for logical consistency:** Since $A \subseteq B$ and $B \subset C$, by transitivity, $A \subseteq C$ must hold (because all elements of $A$ are in $B$, and all elements of $B$ are in $C$). This contradicts the condition $A \not\subset C$. 4. **Conclusion:** It is **not possible** to find such sets $A$, $B$, and $C$ that satisfy all three conditions simultaneously. **Final answer:** Not possible.