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.

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

Answer 1

The correct option is B

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

i) The people who read H but not T are elements of the set H - T.

Consider the Venn Diagram above.

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

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

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

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

$=120-30=90$

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

$=50-30=20$

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

$=120+50-30$

$=140$

$n\left(\right(H\cup T{)}^{\prime })=n(U)-n(H\cup T)$

$=200-140$

$=60$