Answer to Question #150013 in Discrete Mathematics for Anne Naisoi

Question

In an engineering class there are 15 students taking chemistry,20 students taking mathematics. Of these students,10 are taking both chemistry and mathematics.How many students are taking either chemistry or mathematics?

Answer 1

Let $A$ denotes the set of students taking chemistry, $B$ denotes the set of students taking mathematics. Then $A\cap B$ be the set of students taking both chemistry and mathematics. It follows that $|A|=15,\ |B|=20,\ |A\cap B|=10.$

The number of students that take mathematics but do not take chemistry is $|B|- |A\cap B|=20-10=10.$ The number of students that take chemistry but do not take mathematics is $|A|- |A\cap B|=15-10=5.$

Therefore, the number of students taking either chemistry or mathematics is $5+10=15$

Answer: 15