Question

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

Answer 1

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