11. In a school of 100 students, there are 63 basketball enthusiasts and 75 football enthusiasts, but not every student necessarily has both of these interests, so the minimum and maximum values for the number of students who love both basketball and football are $\qquad$.
11. 38,63 Hint: Let $I=\{$ all students $\}, A=\{$ students who love basketball $\}, B=\left\{\frac{1}{3}\right.$ students who love football $\}$, then $|I|=100$, $|A|=63,|B|=75$, by the principle of inclusion-exclusion, $|I|=|A|+|B|-|A \cap B|+|\overline{A \cup B}|,|A \cap B|=|A|+|B|-|I|+$ $|\overline{A \cup B}| \geqslant|A|+|B|-|I|=38$, and $|A \cap B| \leqslant \min \{|A|,|B|\}=63$.