1. **Stating the problem:** How to use the concept of chevauchements (overlaps) in problem-solving. 2. **Understanding chevauchements:** Chevauchements represent the common part shared by two or more sets or shapes, mathematically expressed as the intersection $A \cap B$. 3. **Using chevauchements in set problems:** To find the overlap between two sets $A$ and $B$, use the formula for the intersection: $$ A \cap B = \{x \mid x \in A \text{ and } x \in B\} $$ This helps identify elements common to both sets. 4. **Using chevauchements in probability:** If $P(A)$ and $P(B)$ are probabilities of events $A$ and $B$, the probability of their overlap (both events occurring) is: $$ P(A \cap B) = P(A) + P(B) - P(A \cup B) $$ This formula accounts for the overlap to avoid double counting. 5. **Using chevauchements in geometry:** When two shapes overlap, the chevauchement is the intersecting area or volume. To find it, calculate the intersection region using geometric formulas or integration. 6. **Example:** If two circles overlap, the chevauchement area can be found using formulas involving the radii and distance between centers. 7. **Summary:** To use chevauchements, identify the overlapping region or elements, apply intersection formulas, and use the result to solve problems involving common parts or shared space.