1. **State the problem:** Given sets $A = \{1, 2, 3\}$, $B = \{2, 3, 5\}$, and $C = \{2, 5\}$, find the Cartesian product $(A - B) \times (B - C)$. 2. **Recall the definitions:** - The set difference $X - Y$ is the set of elements in $X$ that are not in $Y$. - The Cartesian product $X \times Y$ is the set of all ordered pairs $(x, y)$ where $x \in X$ and $y \in Y$. 3. **Calculate $A - B$:** $A - B = \{x \in A : x \notin B\} = \{1, 2, 3\} - \{2, 3, 5\} = \{1\}$. 4. **Calculate $B - C$:** $B - C = \{x \in B : x \notin C\} = \{2, 3, 5\} - \{2, 5\} = \{3\}$. 5. **Form the Cartesian product:** $$(A - B) \times (B - C) = \{1\} \times \{3\} = \{(1, 3)\}.$$ **Final answer:** $$(A - B) \times (B - C) = \{(1, 3)\}.$$