1. 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
(i) The collection of all months of a year beginning with the letter J is a collection of objects that is well defined because one can identify the month which belongs to this collection.
Hence, this collection is a set.
(ii) The collection of the ten most talented writers of India is not a very well defined collection as this is the question of talent and talent varies from person to person. It is not a well defined collection.
Hence, this collection is not a set.
(iii) A team of eleven best cricket batsmen of the world is not a very well defined collection again as this is also a question of talent and talent varies from person to person. It is not a well defined collection.
Hence, this collection is also not a set.
(iv) The collection of all boys in your class is a well defined collection as we are able to identify the boy easily who belong to this collection.
Hence, this collection is a set.
(v) The collection of all natural numbers less than 100 is a well defined collection as we can represent all these natural numbers. We can easily find the number which belongs to this collection.
Hence, this collection is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is a well defined collection as we can easily identify the books in this collection.
Hence, this collection is a set.
(vii) The collection of all even integers is a well defined collection because we can easily find the integer which belongs to this collection.
Hence, this collection is a set.
(viii) The collection of questions in this Chapter is a well defined collection we can easily find which question belongs to this chapter.
Hence, this collection is also a set.
(ix) A collection of most dangerous animals of the world is not a well defined collection because this is a quality which can vary from animal to animal.
Hence, this collection is not a set.
Answer:
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Step-by-step explanation:
(i) The collection of all months of a year beginning with J is {J anuary, June, July}, which is well defined and hence it forms a set.
(ii) The collection of most talented writers of India is not well defined because opinions about ‘most talented writers’ vary from person to person and hence it does not form a set.
(iii) A team of eleven best-cricket batsmen of the world is not well defined because opinions about ‘best-cricket batsmen’ vary from person to person and hence it does not form a set.
(iv) The collection of all boys in your class is well defined and hence it forms a set.
(v) The collection of all natural numbers less than 100 is {1, 2, 3, 4,…………, 99}, which is well
defined and hence it forms a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is well defined and hence it forms a set.
(vii) The collection of all even integers is {…………..,-4, -2, 0, 2, 4,……….. } which is well defined and hence it forms a set.
(viii) The collection of questions in this chapter is well defined and hence it forms a set.
(ix) A collection of most dangerous animals of the world is not well defined because opinions about ‘most dangerous animals’ vary from person to person and hence it does not form a set.
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