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