1. **State the problem:** We have a survey of 120 college students who like three brands of mineral water: Voltic, Silver, and Deep. Given the numbers of students who like each brand and their intersections, we want to find the number of students who like at least one of the three brands. 2. **Given data:** - Total students surveyed: 120 - Like Voltic mineral water: 52 - Like Silver mineral water: 58 - Like Deep mineral water: 58 - Like both Voltic and Silver: 25 - Like both Silver and Deep: 18 - Like both Voltic and Deep: 21 - Like all three brands: 13 3. **Formula used:** To find the number of students who like at least one brand, use the principle of inclusion-exclusion: $$|V \cup S \cup D| = |V| + |S| + |D| - |V \cap S| - |S \cap D| - |V \cap D| + |V \cap S \cap D|$$ 4. **Substitute the values:** $$|V \cup S \cup D| = 52 + 58 + 58 - 25 - 18 - 21 + 13$$ 5. **Calculate step-by-step:** $$52 + 58 + 58 = 168$$ $$25 + 18 + 21 = 64$$ 6. **Apply inclusion-exclusion:** $$|V \cup S \cup D| = 168 - 64 + 13$$ 7. **Simplify:** $$168 - 64 = 104$$ $$104 + 13 = 117$$ 8. **Interpretation:** 117 students like at least one of the three brands of mineral water. 9. **Optional:** Number of students who do not like any of the three brands: $$120 - 117 = 3$$ **Final answer:** $$\boxed{117}$$ students like at least one of the three brands of mineral water.