Chapter 1 introduces the concept of sets as collections of well-defined objects, illustrating this with examples. Two methods of representing sets are discussed: roster form, which lists elements, and set-builder form, which defines elements by a common property. The chapter also explains the concept of a universal set, containing all elements of other sets.

1. SETS
Chapter 1
Introduction

2. A set is a collection of well-defined objects.
Consider the two statements:
(i) The collection of all beautiful flowers in Ooty Rose Garden.
(ii) The collection of all old men in Tamilnadu.
“The collection of all men in Tamilnadu of age greater than 70”.
“The collection of all red flowers in Ooty Rose Garden”

4. “The symbol ∈should be used between an element
and a set and it should not be used between two sets”

6. There are two methods of representing a set :
(i) Roster or tabular form
(ii) Set-builder form.
In roster form, all the elements of a set are listed, the
elements are being separated
by commas and are enclosed within braces { }.
For example, the set of all even
positive integers less than 7 is described in
roster form as {2, 4, 6}.

7. (a) The set of all natural numbers which divide 42 is
{1, 2, 3, 6, 7, 14, 21, 42}.

8. ii) In set-builder form, all the elements of a set
possess a single common property
which is not possessed by any element outside
the set.
For example, in the set
{a, e, i, o, u}, all the elements possess a common property, namely,
each of them
is a vowel in the English alphabet, and no other letter possess this
property. Denoting
this set by V, we write
V = {x : x is a vowel in English alphabet}

9. The above description of the set V is read as “the set of all x
such that x is a vowel of the English alphabet”. In this
description the braces stand for “the set of all”, the colon
stands for “such that”.
V = {x : x is a vowel in English alphabet}
A = {x : x is a natural number and 3 < x < 10} is read as “the
set of all x such that x is a natural number and x lies between
3 and 10

22. A universal set is a set which contains all
the elements or objects of other sets,
including its own elements.

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