In a class of 80 students 53 study art,60 study biology,36 study art and biology,34 study art and chemistry,6 study biology only and 18 study biology but not chemistry.Illustrate the information on a Venn diagram.Determine the number of student study (i)art only (ii)chemistry.

Answer 1

Make the Venn diagram. Let
a = # who study art only
b = # who study biology only
c = # who study chemistry only
x = # who study only art and biology
y = # who study only art and chemistry
z = # who study only biology and chemistry
n = # who study all three subjects
Now, we know that
a+x+y+n = 53
b+x+z+n = 60
x+n = 36
y+n = 34
b = 6
b+x = 18
Solving that, we get
a = 7
Note that nowhere does c get used. So, since the sum of all the other numbers is 77, if we assume that all 83 students study something, then 6 study only chemistry.