1. The problem is to understand the definition and notation of sets. 2. A set is a well-defined collection of distinct objects, considered as an object in its own right. 3. The objects in a set are called elements or members. 4. Sets are usually denoted by capital letters, e.g., $A$, $B$, $C$. 5. Elements of a set are listed inside curly braces, e.g., $A = \{1, 2, 3\}$ means set $A$ contains elements 1, 2, and 3. 6. The notation $x \in A$ means element $x$ is in set $A$. 7. The notation $x \notin A$ means element $x$ is not in set $A$. 8. Sets can be described by listing elements or by a property, e.g., $B = \{x : x \text{ is an even number}\}$. 9. Important sets include the empty set $\emptyset$ which has no elements. 10. Summary: Sets are collections of distinct elements, denoted by capital letters, with elements inside curly braces, and membership indicated by $\in$ or $\notin$. Final answer: Sets are collections of distinct elements denoted by capital letters and written as $A = \{a, b, c\}$ with membership $x \in A$ meaning $x$ is an element of $A$.