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.
(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.
Solution and Explanation
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects
because one can definitely identify a month that belongs to this collection.
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 you can definitely identify a boy
who belongs to this collection.
Hence, this collection is a set.
(v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely
identify a number that 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 because one can
definitely identify a book that belongs to this collection.
Hence, this collection is a set.
(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even
integer that belongs to this collection.
Hence, this collection is a set.
(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a
question that belongs to this chapter.
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 dangerousness of an animal can vary from person to person.
Hence, this collection is not a set.
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Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
Read More: Set Theory
Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
Read Also: Set Operation
Cardinal Number of a Set:
The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
Read More: Types of Sets