Page 82 - ICSE Math 7

Representation of sets
A set can be represented in two ways.
(a) Roster or Tabular form (b) Set-builder or Rule form

Roster or tabular form
In this form, a set is represented by writing its members inside curly brackets, separated by commas.
For example,

(a) The set A of first three even natural numbers is given by Maths Info
A = {2, 4, 6}.

(b) The set X of all the vowels is given by X = {a, e, i, o, u}. The order of elements of a set
is not important.
Set-builder or rule form
In this form, a set is represented by writing a common property describing the elements in curly
brackets. For example, set Y of natural numbers less than 10 is given by
Y = {x | x is a natural number less than 10} or Y ={x : x is a natural number less than 10}

The vertical bar ‘|’ or colon ‘:’ is read as ‘such that’. So the above set is read as ‘Y’ is the set of elements
like x such that x is a natural number less than 10.

Example 2: Write the following sets in the roster form.
(a) The set of letters of the word ARITHMETIC.
(b) The set X of even prime numbers.
(c) The set Y of all the integers between –2 and 3.
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(d) A = {x | x < 5, x ∈ N}
Solution: (a) Distinct letters in the word ARITHMETIC are A, R, I, T, H, M, E and C. Therefore,
the required set is given by {A, R, I, T, H, M, E, C}.
(b) The only even prime number is 2. Therefore, X = {2}
(c) The integers between –2 and 3 are –1, 0, 1 and 2. Therefore, Y = {–1, 0, 1, 2}
(d) Natural numbers whose square is less than 5 are 1 and 2. Therefore, A = {1, 2}

Example 3: Write the following sets in the set-builder form.
(a) X = {3, 6, 9, 12, 15, ...} (b) Y = {1, 2, 3, 6}

(c) A = {2, 3, 5, 7, ...} (d) X = {0, 1, 4, 9, 16, 25}
Solution: (a) X = {x | x is a multiple of 3} or X = {x | x = 3n, n ∈ N}
(b) Y = {x | x is a factor of 6}

(c) A = {x | x is a prime number}
(d) X = {x | x is the square of a whole number less than 6}
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{x | x = n , n ∈ W, n ≤ 5}

Exercise 6.1

1. Which of the following collections are sets?
(a) Days of a week. (b) All the intelligent girls of your class.
(c) All the whole numbers. (d) Last four English letters.

(e) Five good players of your school. (f) Even positive integers greater than 7.

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