Question

Which of the following are sets? Justify your answer.
( i ) The collection of all whole numbers less than 10.
( ii ) The collection of good hockey players in India.
( iii ) The collection of all questions in this chapter in this book.
( iv ) The collection of all difficult chapters in this book.
( v ) The collection of hindi novels written by Munshi Pem Chand.
( vi ) A team of 11 best players of India.
( vii ) The collection of all the months of the year whose names begin with the letter M.
( viii ) The collection of all interesting books.
( ix ) The collection of all short boys of your class.
( x ) The collection of all those students in your class whose ages exceed 15 years.

Answer 1

Hint: Sets are the collection of objects which are well defined i.e. objects in a set whose characteristics and nature can be judged on some parameters. So, for collection to be called set, it should be well defined for all objects it is containing. So, we will see each part and will check which are well defined which are not.

Complete step-by-step answer:
( i ) All whole numbers which are less than 10 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 which are finite also.
Hence, The collection of all whole numbers less than 10 is a set.

( ii ) There is no such parameter or criteria on which we can decide whether a given hockey player of India is good or not. So, The collection of good hockey players in India is not a set.

( iii ) From a particular chapter, we can easily decide whether this question belongs to this chapter or not. Hence, the collection of all questions in this chapter in this book is a set.

( iv ) For different people, the level of difficulty of a particular chapter is unclear. Hence, the collection of all difficult chapters in this book is not a set.

( v ) There are finite numbers of hindi novels written by munshi premchand. Hence, the collection of hindi novels written by Munshi Pem Chand is a set.

( vi ) There is no such parameter or criteria on which we can decide whether a given Indian player is best or not. Hence, A team of 11 best players of India is not a set.

( vii ) The collection of all the months of the year whose names begin with the letter M are March and May. Hence, the collection of all the months of the year whose names begin with the letter M is a set.
( viii ) ) There is no such parameter or criteria on which we can decide whether a given book is interesting or not. Hence, the collection of all interesting books is not a set.

( ix ) as there is no specific height decided to guess whether the boy in your class is short or not. Hence, the collection of all short boys of your class is not a set.

( x ) In a class there are a finite number of students and can be decided whether their age is above 15 or not. Hence, The collection of all those students of your class whose ages exceeds 15 years is a set.


Note: There must be a fixed and well defined parameter on which objects belonging to the collection are defined. Then only the collection is called set. Sets can be finite or infinite so it does not depend upon the number of objects in the collection.