1. The problem is to practice basic set theory operations such as union, intersection, difference, and complement. 2. Important formulas and rules: - Union: $A \cup B = \{x : x \in A \text{ or } x \in B\}$ - Intersection: $A \cap B = \{x : x \in A \text{ and } x \in B\}$ - Difference: $A - B = \{x : x \in A \text{ and } x \notin B\}$ - Complement: $A^c = \{x : x \notin A\}$ 3. Example question: Given sets $A = \{1,2,3,4\}$ and $B = \{3,4,5,6\}$, find: - $A \cup B$ - $A \cap B$ - $A - B$ - $B - A$ 4. Solution: - $A \cup B = \{1,2,3,4,5,6\}$ because it includes all elements in either $A$ or $B$. - $A \cap B = \{3,4\}$ because these elements are in both $A$ and $B$. - $A - B = \{1,2\}$ because these elements are in $A$ but not in $B$. - $B - A = \{5,6\}$ because these elements are in $B$ but not in $A$. 5. Explanation: Set operations help us combine or compare groups of elements. Union combines all unique elements, intersection finds common elements, and difference finds elements in one set but not the other. This practice question covers fundamental set theory concepts useful for further study.