Question

In a college, 150 students are randomly selected. 73 like tea, 87 like coffee, and 48 like both tea and coffee. 
How many students like only tea and only coffee?
How many students like neither tea nor coffee?
Draw a Venn-Diagram!

Answer 1

Let U be the set of all students who took part in the survey.

Let T be the set of students taking tea.

Let C be the set of students taking coffee.

n(U)=600,n(T)=150,n(C)=225,n(T∩C)=100

To find: Number of student taking neither tea nor coffee i.e., we have to find n(T  

′

∩C  

′

).

n(T  

′

∩C  

′

)=n(T∪C)  

′

 

=n(U)−n(T∪C)

=n(U)−[n(T)+n(C)−n(T∩C)]

=600−[150+225−100]

=600−275

=325

Hence, 325 students were taking neither tea nor coffee.