Out of 200 students who are trying to improve their vocabulary, 120 students read newspaper H, 50 read newspaper T and 30 read both newspaper H and T. Find the number of students
i) who read H but not T
ii) who read T but not H
iii) who don't read any newspaper.
90, 20, 60
Let U be universal set consisting of all students
Set H denote the students who read newspaper H.
Set T denote the students who read newspaper T.
Given, n(∪)=200, n(H)=120, n(T)=50, n(H∩T)=30.
i) The people who read H but not T are elements of the set H - T.
Consider the Venn Diagram above.
H=(H−T)∪(H∩T)
So, n(H)=n(H−T)+n(H∩T).
(since H - T and H∩T are disjoint)
⇒n(H−T)=n(H)−n(H∩T)
=120−30=90
n(T−H)=n(T)−n(H∩T)
=50−30=20
n(H∪T)=n(H)+n(T)−n(H∩T)
=120+50−30
=140
n((H∪T)′)=n(U)−n(H∪T)
=200−140
=60