What is a well-Defined Set?

Set
A set is collection of well defined objects.

In the above definition the words set and collection for all practical purposes are Synonymous. We have really used the word set to define itself.

We encounter sets in many different ways every day of our lives. A set is a collection of objects. which are called elements or members of the set. For example, the United States is a collection, or set, of 50 states plus the District of Columbia. The 50 individual states plus the District of Columbia are the members or elements of the set that is called the United States.

A set is well defined if its contents can be clearly determined. The set of U.S. presidents is a well-defined set because its contents, the presidents. can be named. The set of the three best movies is not a well—defined set because the word best is interpreted differently by different people. In this text. we use only welt-defined sets.

Three methods are commonly used to indicate a set: (1) description. (2) roster form. and (3) set-builder notation.

The method ofindicating a set by description is illustrated in Example 1.

📌 Example 1: Description of Sets
Write a description of the set containing the elements Monday. Tuesday, Wednesday, Thursday, Friday, Saturday. Sunday.
✍ Solution:
The set is the days of the week.

📌 Question 1. Which of the following are sets? Justify your answer.
(i) The collection of all months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of Canada.
(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 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 Canada 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-deflned collection because the criteria for determining the dangerousness of an animal can vary from person to person.
Hence, this collection is not a set.

🧠 Enrichment for your comprehension:
Some Sets which are well-Defined.

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