INTRODUCTION TO SET

We often deal with a group or a collection of objects,  such as a collection of books, a collection of English alphabets, a group of students, a list of states in a country, a collection of coins, etc. Set may be considered as a mathematical way of representing a collection or a group of objects.

Definition of Set :

A set is a collection of well defined objects. The objects of a set are called elements or members of the set.

The main property of a set is that it is well defined. This means that given any object, it must be clear whether that object is a member (element) of the set or not.

Generally, sets are named with the capital letters A, B, C, etc. The elements of a set are denoted by the small letters a, b, c, etc.

Examples of Sets in Daily Life :

  • Students in our class room
  • Collection of animals in the world
  • Collection of fruits
  • Collection of vegetables

Which of the following collection are sets ? Justify your answer.

Question 1 :

A collection of all natural numbers less than 50.

Answer :

If forms a set. The set will have the following elements.

A = {1, 2, 3, 4, 5, ...................50}

Question 2 :

A collection of good hockey players in America

Answer :

If doesn't form a set. Because the term "Good player" is vague and it is not well defined.

However a collection of players of hockey is a set.

Question 3 :

A collection of all girls in our class.

Answer :

If forms a set. The elements of the above set is the names of those girls in the class.

Question 4 :

A collection of prime numbers less than 30

Answer :

If forms a set.  The set will have the following elements.

A = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 }

Question 5 :

A collection of ten most talented mathematics teachers.

Answer :

If doesn't form a set. Because the term "Most talented" is vague and it is not well defined.

However a collection of players of hockey is a set.

In this chapter we will have frequent interaction with some sets, so we reserve some letters for these sets as listed below. :

N  :  The set of natural numbers

Z  :  The set of integers

Z+  :  The set of all positive integers

Q  :  The set of all rational numbers

Q+  :  The set of all positive rational numbers

R+  :  The set of all real numbers

R+  :  The set of all positive real numbers

C  :  The set of all complex numbers

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