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
Let U be universal set consisting of all students
Set A denote the students who read newspaper H.
Set B denote the students who read newspaper T.
Here n(U) = 200, n(H) = 120, n(T) = 50, n(H ∩ T) = 30
i) H but not T is nothing but H - T
Consider the Venn Diagram above.
H = (H - T) U (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(who don't read any newspaper) = n(U) - n(H) - n(T) + n(H ∩ T)
= 200 - 120 - 50 +30 = 60