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. Which of the following are correct.

• A. 30,20,60
• B. 90, 20, 60
• C. 90, 20, 30
• D. 20,30,60

Answer 1

Answer: (A), (C), (D)

The correct options are
A

30,20,60

C

90, 20, 30

D

20,30,60

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 $n(\cup )=200,n\left(H\right)=120,n\left(T\right)=50,n(H\cap T)=30$

i) H but not T is nothing but H - T

Consider the Venn Diagram above.

$H=(H-T)\cup (H\cap T)$

So, $n\left(H\right)=n(H-T)+n(H\cap T)$

(since H - T and $H\cap T$ are disjoint)

$n(H-T)=n\left(H\right)-n(H\cap T)$

= 120 - 30 = 90

$n(T-H)=n\left(T\right)-n(H\cap T)$

= 50 - 30 = 20

$n(H\cup T{)}^{{}^{\prime }}=n(\cup )-n(H)-n(T)+n(H\cap T)$

= 200 - 120 - 50 +30 = 60