Which of the following are sets ? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.

Solution:

(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection.

Hence, this collection is a set.

(ii) The collection of ten most talented writers of India is not a well-defined collection because the criteria for determining a writer’s talent may vary from person to person.

Hence, this collection is not a set.

(iii) A team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsman’s talent may vary from person to person.

Hence, this collection is not a set.

(iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection.

Hence, this collection is a set.

(v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection.

Hence, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify a book that belongs to this collection.

Hence, this collection is a set.

(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection.

Hence, this collection is a set.

(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter.

Hence, this collection is a set.

(ix) The collection of the most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person.

Hence, this collection is not a set

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NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.1 Question 1

Which of the following are sets ? Justify your answer. (i) The collection of all the months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers (viii) The collection of questions in this Chapter. (ix) A collection of most dangerous animals of the world.

Summary:

We are asked to determine which of the given collections is/are a set. We found that

(i) The collection of all the months of a year beginning with the letter J is a set.
(ii) The collection of ten most talented writers of India is not a set.
(iii) A team of eleven best cricket batsmen of the world is not a set.
(iv) The collection of all boys in your class is a set.
(v) The collection of all natural numbers less than 100 is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is a set.
(vii) The collection of all even integers is a set.
(viii) The collection of questions in this Chapter is a set.
(ix) A collection of most dangerous animals of the world is not a set.