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NOTATIONS FOR A SET:
A set can be represented by two methods:
ROSTER METHOD:
- ROSTER METHOD
- BUILDER 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.
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.
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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