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 number of students who are enthusiasts of both basketball and football are $\qquad$ .
11. 38,63 Hint: Let $I=\{$ all students $\}, A=\{$ students who like basketball $\}, B=\{$ students who like 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 $|A \cap B| \leqslant \min \{|A|,|B|\}=63$.