Answer
369
Work Step by Step
Let $A$ denote the set of students that have taken a course in calculus, and $B$ denote the set of students that have taken a course in discrete mathematics. We are given that $|A|=345$, $|B|=212$, and $|A\cap B|=188$. We are looking for the number of students that have taken either a course in calculus or a course in discrete mathematics, which is $|A\cup B|$. By the Principle of Inclusion-Exclusion, $|A \cup B|=|A|+|B|-|A\cap B|=345+212-188=369$.
