Which of the following are sets ? Justify your answer. (i)...

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 most dangerous animals of the world.

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 most dangerous animals of the world.

Key Concepts

Well-Defined Collection

In set theory, a set must be a collection in which it is possible to determine unambiguously whether any given object belongs to it. The concept emphasizes that every element should be clearly identifiable based on a definitive property or rule.

Precise Specification of Elements

A key characteristic of a set is that the elements are precisely described or enumerated. This precision ensures that there is no confusion over whether an object is a member of the set, which is fundamental to its proper definition in mathematics.

Ambiguity and Subjectivity in Definitions

When a collection is defined using subjective terms or vague criteria—such as 'most talented' or 'best'—it results in ambiguity. Such collections do not meet the strict requirements of set theory because their criteria for membership are not explicitly clear or universally agreed upon.

Transcript

00:01 The collection of all months of year beginning with the letter j so here it is a well -defined collection of objects because we have three months which is beginning with the letter j j j -juary june july and one can definitely identity a month that belongs to this collection hence the collection is a set so it is our answer the collection of ten most talented writer of india so here we can say it is not a well -defined collection of objects because the criteria of determining a writer talents may worry from person to person hence these collection is not a set so it is our answer for part second now we parts sole part third a team of 11 best cricket best men of the world so here we can say it is not a well -defined collection of objects because the criteria of determining a best man talent may vary from person to person hence this collection is not a set so it is a answer for part third now is whole part four the collection of all boys in your class so here it is a well -defined collection of check because you can definitely identify a boy who belongs to this collection.

03:50 Hence, this collection is a set.

04:01 Part 5, the collection of all natural numbers less than 100.

04:06 So here you can see that it is well defined collection because one can definitely identify a number that belongs to this collection.

04:15 So here we can say this collection is a set, a collection of novel written by the writer munshi prem chen.

04:37 So here you can see that it is a well -defined collection because one can definitely identify a number that belongs to this collection.

04:47 And here a book that belongs to this collection.

04:50 Hence the collection is a sets.

04:58 The collection of all even integers, so here we can say it is a well -defined collection of object because one can definitely identify an even integers that belongs to these collections...

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