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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

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B

90, 20, 60

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C

90, 20, 30

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D

20, 30, 60

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Solution

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()=200, n(H)=120, n(T)=50, n(HT)=30.

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

Consider the Venn Diagram above.

H=(HT)(HT)

So, n(H)=n(HT)+n(HT).

(since H - T and HT are disjoint)

n(HT)=n(H)n(HT)

=12030=90

n(TH)=n(T)n(HT)

=5030=20

n(HT)=n(H)+n(T)n(HT)

=120+5030

=140

n((HT))=n(U)n(HT)

=200140

=60


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