Question

Which of he 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 batsman of the world
(iv) The collection of all body in your class
(v) The collection of all natural numbers less than 100
(vi) A collection of novels written by the writer Munshi Premchand
(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 1

(i) Months starting from J are January, June, July. These months are well-defined
Therefore, the collection of all months starting from J is a set
(ii) `because` It has no scale to say whether a writer is talented or not i.e., this collection is not well-defined. Thus, the collection of ten most talented writers of India is not a set
(iii) `because` There is no scale to decide whether a batsman is best or not i.e., this collection is not well defined. thus the collection of a team of eleven best-cricket batsmen is not a set
(iv) The number of boys in a class is fixed, so their collection is well-defined. Thus, the collection of all boys in your class is a set
(v) Collection of all natural numbers less than 100 is
`{1,2,3,4,....,99}`
which is well-defined. Thus, the collection of all natural numbers less than 100 is a set
(vi) `because` The number of novels written by Munshi Premchand is definite, which is well-defined. Thus, this collection is a set.
(vii) The properties of the collection of integers 2,4,6,8,10,12.... is definite and well-defined. Thus, the collection of even integers is a set.
(viii) Each question given in the chapter is well defined. Thus, this collection is a set
(ix) There is no scale to decide whether an animal is dangerous or not. Thus, the collection of most dangerous animals of the world is not a set.