# Roster, Builder Method

NOTATIONS FOR A SET:

A set can be represented by two methods:
• ROSTER METHOD
• BUILDER METHOD
ROSTER METHOD:

In this method the elements of a set are separated by commas and are enclosed within curly brackets { }. For example:

A = {1, 2, 3, 4, 5, 6} is a set of numbers.

B = {Sunny, Joy, Kartik, Harish, Girish} is a set of names.

C = {a, e, i, o, u} is a set of vowels.

D = {apple, banana, guava, orange, pear} is a set of fruits.

Listing the elements in this way is called Roster method. In this method, it is not necessary for the elements to be listed in a particular order. The elements of the set can be written just plainly, separated by commas and in any order.

BUILDER METHOD:

This method is also called Property method. In Builder method, a set is represented by stating all the properties which are satisfied by the elements of that particular set only.

For example:

If A is a set of elements less than 0, then in Builder method it will be written as

A = {x: x < 0}, this statement is read as "the set of all x such that x is less than 0"

If A is a set of all real numbers less than 7, then in Builder method it is written as A = {x R: x < 7}

Similarly,

A = {2i: i is an integer} is a set of all even integers.

A = {x R: x ≠ 2} is a set of all real numbers except 2.

A = {x R: x > 3 and x < 7} is a set of real numbers greater than 3 but less than 7.

A = {x Z: x > 6} is a set of integers greater than 6.

A = {x Z: 2x + 1} is a set of all odd integers.

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