1. The problem is to understand and perform operations on sets. 2. Common set operations include union ($A \cup B$), intersection ($A \cap B$), difference ($A - B$), and complement ($A^c$). 3. The union of two sets $A$ and $B$ is the set of elements in $A$ or $B$ or both: $$A \cup B = \{x : x \in A \text{ or } x \in B\}$$ 4. The intersection of two sets $A$ and $B$ is the set of elements common to both: $$A \cap B = \{x : x \in A \text{ and } x \in B\}$$ 5. The difference $A - B$ is the set of elements in $A$ but not in $B$: $$A - B = \{x : x \in A \text{ and } x \notin B\}$$ 6. The complement $A^c$ is the set of elements not in $A$ relative to a universal set $U$: $$A^c = \{x : x \in U \text{ and } x \notin A\}$$ 7. To perform these operations, list the elements of each set and apply the definitions above. This explanation covers the basic operations on sets with formulas and definitions.