1. The problem is to understand and solve questions related to set operations such as union, intersection, difference, and complement. 2. Important formulas and definitions: - 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 from both sets. - $A \cap B = \{3,4\}$ because these elements are common to both sets. - $A - B = \{1,2\}$ 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, difference finds elements in one set but not the other, and complement finds elements not in the set relative to a universal set. Final answers: - $A \cup B = \{1,2,3,4,5,6\}$ - $A \cap B = \{3,4\}$ - $A - B = \{1,2\}$ - $B - A = \{5,6\}$