A set is an unordered collection of objects, called elements or members of the set. A set is said to contain its elements.We write a ∈ A to denote that a is an element of the set A. The notation a ∈ A denotes that a is not an element of the set A.
Generally sets are denoted by capital letters A, B, C and etc. For example
A={a,b,c,d,e,f,g,h,i}
The ordering of elements in a set does not change the set. For example:
A={1,2,3,5} and B={5,1,2,3} equal sets.
In general the set can be expressed in two ways. i.e. Tabular method (Roster Method) and Set-Builder Method (Specification Method) .
Tabular Method
Expressing the elements of a set within a parenthesis where the elements are separated by commas is known as tabular method, roster method or method of extension. Consider the following examples:
A={1,2,4,5,3,89,56,45}
B={a,b,c,d,e,f,h,i,o,u}
Set Builder Method
Expressing the elements of a set by a rule or formula is known as set-builder method, specification method or method of intension. Mathematically
S={ x | P(x) }
Where P(x) is the property that describes the elements of the set. The symbol | stands for ‘such that’ . Consider the following examples:
A={ x | x=2n; 0≤n≤16, n∈I}
= {0,2,4,6 ,8,10,12,14,16}
S = {x | x is a positive integer less than 100}
Some Important Sets
B = Boolean values = {true,false}
N = natural numbers = {0, 1, 2, 3, ……. }
Z = integers = {…..,-3,-2,-1, 0, 1, 2, 3, …….}
Z+ = positive integers = {1, 2, 3, …….}
R = set of real numbers
R+ = set of positive real numbers
C = set of complex numbers
Q = set of rational numbers
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