Question

In a class of 30 students, 11 students like mathematics, 12 students like geography, and 12 students do not like mathematics nor geography. How many students like mathematics and geography

Answer 1

Let $A$ be a set of students that like mathematics, $B$ be a set of students that like geography. Then the number of students that like mathematics or geography is $|A\cup B|=30-12=18$. Taking into account that $|A|=11$ and $|B|=12$, by combinatorial Inclusion-Exclusion Principle we conclude that the number of students that like mathematics and geography is $|A\cap B|=|A|+|B|-|A\cup B|= 11+12-18=5.$