Answer to Question #99864 in Discrete Mathematics for Ahmed

Question

There are 60 science student in a secondary school 35 of whom study chemistry and 30 study technical drawing.12 out of those students study biology and chemistry but not technical drawing.10 study chemistry but neither biology nor technical drawing,11study only technical drawing and neither biology nor chemistry,10 only study chemistry and technical drawing only. How many students study all the three subjects?

Answer 1

Among 35 people who study chemistry, 10 study only chemistry, 10 only chemistry and technical drawing, 12 only chemistry and biology. Consider all possible options for studying subjects given that the student is studying chemistry:

The student only studies chemistry and does not study other subjects (10);

The student only studies chemistry and biology and does not study the technical drawing (12);

The student only studies chemistry and technical drawing and does not study biology(10);

Student studies all subjects.

These sets do not intersect since the conditions exclude the student’s ability to be in two sets simultaneously and includes all possible options, provided that the student is studying chemistry

Thus, students study all the three subjects is equal to

$$N=35−10−10−12=3$$

Answer. 3 students.