Page 104 - ICSE Math 6

(c) The given collection is not a set as there is no standard to decide the level of
difficulty of problems and hence the elements (i.e., problems) of the set are not
well-defined.
(d) The collection of distinct letters, i.e., M, U, B, A, I is a set.

Example 2: Let X be the set of the letters of the word AUGUST and Y be the set of the letters of
the word ENGLISH. Fill in the blanks by writing ∈ or ∉.
(a) E ____ X (b) U ____ Y (c) G ____ X (d) I ____ Y

Solution: (a) E ∉ X (b) U ∉ Y (c) G ∈ X (d) I ∈ Y

Representation of Sets
To represent a set, we list its members (elements). There are two ways of representing a set:

(a) Roster or tabular form method
(b) Rule of set-builder form method

Roster or tabular form method
In this method, a set is represented by writing all of its members inside Maths Info
the curly braces { }, separated by commas. For example, Any change in the order of
(a) The set X of the first five months of a year is given by writing the elements of a set
X = {January, February, March, April, May}. does not change the set.

(b) The set Y of all the vowels in the word PAPER is given by Y = {A, E}.
Rule or set-builder form method
In this method, all the members of a set are not written inside the curly braces. Instead, a statement
or common property describing the elements is written inside the curly braces. For example, the set
Y of whole numbers less than 10 is given by
Y = {x | x is a whole number less than 10} or Y = {x : x is a whole number less than 10}.
The vertical bar ‘ | ’ or colon ‘ : ’ placed between the two xs stands for ‘such that’. (This is read as ‘Y
is the set of elements x such that x is a whole number less than 10’.)
Let’s write some important sets in the roster and set-builder forms.
(a) The set N of all the natural numbers.
N = {1, 2, 3, 4, …} (Roster form)
= {x | x is natural number} (Set-builder form)
(b) The set W of all the whole numbers.
W = {0, 1, 2, 3, …} (Roster form)
= {x | x is a whole number} (Set-builder form)
(c) The set Z or I of all the integers.
Z = {…, –3, –2, –1, 0, 1, 2, 3, …} (Roster form)
= {x | x is an integer} (Set-builder form)

Different statements can be used to represent the same set in set-builder form.

Example 3: Write the following sets in the roster form.

(a) The set X of all the odd natural numbers less than 9.
(b) The set A of all the consonants in the word ROSTER.
(c) The set Y of all the integers between –3 and 3.

88