Question

Which of the following are sets?
$i.)$ 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.
$xi.)$ A collection of most dangerous animals of the world.

Answer 1

$i.$ The collection of all months of a year beginning with the letter J is well-defined collection of objects as one can identify a month which belongs to this collection.
So, the above set can be written in roster form as {January, June, July}


$ii.$ The collection of ten most talented writers of India is not a well-defined collection as the criteria to determine a writer’s talent may differ from one person to another.
Hence, this collection is not a set.


$iii.$ A team of eleven best cricket batsmen of the world is not a well-defined collection as the criteria to determine a batsman’s talent may vary from one person to another.
Hence, this collection is not a set.


$iv.$ The collection of all boys in your class is a well-defined collection as you can identify a boy who belongs to this collection.
The above set can be written in set builder form as
{$x:x$ is a boy in your class}


$v.$ The collection of all natural numbers less than $100$ is a well-defined collection as one can find a number which belongs to this collection.
The above set can be written in set builder form as
$\{x:x\in N\text{and}x<100\}$


$vi.$ A collection of novels written by the writer Munshi Prem Chand is a well-defined collection as one can find a book which belongs to this collection.
The above set can be written in set builder form as
{$x:x$ is a novel written by the writer Munshi Prem Chand}


$vii.$ The collection of all even integers is a well-defined collection as one can find an integer which belongs to this collection.
The above set can be written in set builder form as
{$x:x=2n,n\in Z$}


$viii.$ The collection of question in this chapter is a well-defined collection as one can find a question which belongs to this chapter.
The above set can be written in set builder form as
{$x:x$ is a question in this chapter}


$ix.$ The collection of most dangerous animals of the world is not a well-defined collection as the criteria to find the dangerousness of an animal can differ from one person to other. Hence, this collection is not a set.