Question:

Which of the following are sets? Justify our answer. 
(i) The collection of all 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.

Updated On: Oct 22, 2023
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Solution and Explanation

(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 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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