Which of the following are sets? Justify our 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.
Answers
Answer:
Step-by-step explanation:
Solution:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects as one can identify a month which belongs to this collection.
Therefore, this collection is a set.
(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.
Therefore, 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.
Therefore, 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.
Therefore, this collection is a set.
(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.
Therefore, this collection is a set.
(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.
Therefore, this collection is a set.
(vii) The collection of all even integers is a well-defined collection as one can find an integer which belongs to this collection.
Therefore, this collection is a set.
(viii) The collection of questions in this Chapter is a well-defined collection as one can find a question which belongs to this chapter.
Therefore, this collection is a set.
(ix) A 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 animal to another.
Therefore, this collection is not a set.