Which of the following are sets? Justify your answer.

Which of the following are sets? Justify your 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.
Answer
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because every person will collect same months which are {January , June , July }.
Hence, collection of all 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 well-defined collection because the choice of selection of ten most talented writers of India may vary from person to person.
Hence, collection of ten most talented writers of India is not a set.

(iii)The collection of A team of eleven best-cricket batsmen of world is not a well-defined collection because the choice of selection of best-cricket batsmen may vary from person to person.
Hence, The collection of A team of eleven best-cricket is not a set.

(iv)The collection of all boys in your class is a well-defined collection because every any boy of a particular class will collect same students.
Hence, collection of all boys in your class is a set.

(v) The collection of all natural numbers less than 100 is a well-defined collection of objects because every person will collect same numbers which are {1 ,2,3 ,4 ..........100 }.
Hence, collection of all natural numbers less than 100 collection is a set.

(vi)A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because Munshi prem Chandra has written some specific books. Each person will collect same books.
Hence, collection of novels written by the writer Munshi Prem Chand is a set.

(vii) The collection of all even integers is a well-defined collection because every person will collect same numbers which are {2 ,4 ,6 ,........... }.
Hence, collection of all even integers is a set.

(viii) The collection of questions in this chapter is a well-defined collection because there are some specific questions in this chapter and every question is a problem.
Hence, the collection of questions in this chapter is a set.

(ix) The collection of most dangerous animals of the world is not a well-defined collection because the choice of selection of most dangerous animals may vary from person to person.
Hence, collection of most dangerous animals of the world is not a set.