Question

In a survey of 60 students, it was found that 25 students stick to the internet,
26 students remain busy with their mobile and 26 students prefer to read extra books.
9 students prefer to sort internet and remain busy with their mobile, 11 students prefer
to sort internet and read extra books, 8 students prefer to remain busy with their
mobile and read extra books and 3 students are engaged in all three activities.
(a) How many students are not engaged in any of the activities?
(b) How many students sort internet only ? S
(c) Do you think the students who are surfing internet quite often wasting their time?
Comment.​

Answer 1

Step-by-step explanation:

Let A be the set of people who read newspaper H.

Let B be the set of people who read newspaper T.

Let C be the set of people who read newspaper I.

Given n(A)=25,n(B)=26, and n(C)=26

n(A∩C)=9,n(A∩B)=11, and (B∩C)=8

n(A∩B∩C)=3

Let U be the set of people who took part in the survey.

(i) n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

=25+26+26−11−8−9+3

=52

Hence, 52 people read at least one of the newspaper.

(ii) Let a be the number of people who read newspapers H and T only.

Let b denote the number of people who read newspapers I and H only.

Let c denote the number of people who read newspaper T and I only.

Let d denote the number of people who read all three newspaper.

Accordingly, d=n(A∩B∩C)=3

Now, n(A∩B)=a+d

n(B∩C)=c+d

n(C∩A)=b+d

∴a+d+c+d+b+d=11+8+9=28

⇒a+b+c+d=28−2d=28−6=22

Hence, (52−22)=30 people read exactly one newspaper.

See answer in attachment hope it helps u....✌