Question

Which of the 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 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 the most dangerous animals of the world.

Answer 1

Hint: In the above given question, analyze each problem provided with a specific condition individually and check whether the data belonging to the definite collection can be easily identified or not.

Complete step-by-step answer:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because any month belonging to this collection can be easily identified.
 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 any boy who belongs to this collection can be easily identified.
Hence, this collection is a set.

(v) The collection of all natural numbers less than $100$ is a well-defined collection because any number belonging to this category can be easily identified.
Hence, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because any book belonging to this collection can be identified definitely.
Hence, this collection is a set.

(vii) The collection of all even integers is a well-defined collection because any even integer belonging to this collection can be easily identified.
Hence, this collection is a set.

(viii) The collection of questions in this chapter is a well-defined collection because any question belonging to this chapter can be easily identified.
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 animal which is dangerous amongst the other animals can vary from animal to animal.
Hence, this collection is not a set.

Note: If the data belonging to a specific collection can be easily identified, then the collection is said to be a set. Whereas if the data belonging to a specific collection is not identified, then the collection cannot be called as a set.