Counting unions

#inclusion-exclusion#union of sets#counting

Statement

In a class of $30$ students, $18$ like math, $15$ like physics, and $8$ like both. How many like at least one of the two subjects?

Hint

$|A\cup B|=|A|+|B|-|A\cap B|$ .

Show solutionHide solution

Formula. $|M\cup P|=18+15-8=25$ .

Conclusion. $25$ students like at least one subject.

Corollary. $5$ students like neither.