1. The problem asks for two difficult problems involving sets. 2. Let's consider the first problem: Given two sets $A$ and $B$, find the set expression for elements that are in $A$ or $B$ but not in both (symmetric difference). 3. The formula for symmetric difference is: $$A \triangle B = (A \cup B) \setminus (A \cap B)$$ This means we take all elements in either $A$ or $B$ and remove those that are in both. 4. For the second problem: Given three sets $A$, $B$, and $C$, find the set of elements that are in exactly two of the three sets. 5. The formula for elements in exactly two sets is: $$ (A \cap B \setminus C) \cup (B \cap C \setminus A) \cup (A \cap C \setminus B) $$ This means we take elements common to each pair but exclude those in the third set. 6. These problems require understanding of union, intersection, set difference, and symmetric difference operations. 7. To solve these, carefully apply the set operations step-by-step, ensuring correct order and exclusion. Final answers: - Symmetric difference: $$A \triangle B = (A \cup B) \setminus (A \cap B)$$ - Elements in exactly two of three sets: $$ (A \cap B \setminus C) \cup (B \cap C \setminus A) \cup (A \cap C \setminus B) $$