NCERT Class 11 Mathematics Solutions: Chapter 1 – Sets Miscellaneous Exercise Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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In Figure Union and Intersection of Sets Are Defined

1. In a group of students students know Hindi, know English and know both. Each of the students knows either Hindi or English. How many students are there in the group?

Answer:

Let be the set of all students in the group.

Consider be the set of all students who know English.

Consider be the set of all students who know Hindi.

Accordingly,

So, there are students in the group.

2. In a survey of people, it was found that people read newspaper read newspaper read newspaper read both read both read both read all three newspapers. Find:

(i) The number of people who read at least one of the newspapers.

(ii) The number of people who read exactly one newspaper.

Answer:

Consider be the set of people who read newspaper .

Consider be the set of people who read newspaper .

Consider be the set of people who read newspaper .

Accordingly,

Consider be the set of people who took part in the survey.

Answer: (i)

Accordingly,

So, people read at least one of the newspapers.

Answer: (ii)

Understanding the Venn Diagram

Consider be the number of people who read newspapers only.

Consider denote the number of people who read newspapers only.

Consider denote the number of people who read newspapers only.

Consider denote the number of people who read all three newspapers.

Accordingly,

Now,

Hence, people read exactly one newspaper.

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