In class of 80 students 53 study Arts 60 study Biology 36 study Arts and Biology 34 study Arts and Chemistry 6 study Biology only and 18 study Biology but not Chemistry.

Question

Illustrate the information in a venn diagram
Determine the number of students who study
a. Arts only
b. Chemistry

Answer 1

To determine the number of students who study Arts only and Chemistry, we first need to find the number of students who study Arts and Chemistry.

Total number of students = 80
Number of students who study Arts = 53
Number of students who study Biology = 60
Number of students who study both Arts and Biology = 36
Number of students who study both Arts and Chemistry = 34
Number of students who study Biology only = 6
Number of students who study Biology but not Chemistry = 18

Let's denote the number of students who study Arts only as x, and the number of students who study both Arts and Chemistry as y.

From the information given:
53 = x + 36 + 34
60 = y + 36 + 18

Solving for x and y:
x = 53 - 36 - 34 = 17
y = 60 - 36 - 18 = 6

Therefore:
a. The number of students who study Arts only = 17
b. The number of students who study Chemistry = 34 + 18 + 6 = 58