1. **State the problem:** We have 120 students in total. Each student plays soccer, gymnastics, or both. 2. **Given data:** - Number of students who play soccer, $|A| = 110$ - Number of students who do gymnastics, $|B| = 113$ - Total number of students, $|A \cup B| = 120$ 3. **Formula used:** To find the number of students who participate in both activities (intersection), we use the formula for the union of two sets: $$|A \cup B| = |A| + |B| - |A \cap B|$$ Rearranged to find the intersection: $$|A \cap B| = |A| + |B| - |A \cup B|$$ 4. **Calculate the intersection:** $$|A \cap B| = 110 + 113 - 120 = 223 - 120 = 103$$ 5. **Interpretation:** 103 students participate in both soccer and gymnastics. This means most students are involved in both activities, given the total number of students is 120.