What is Set?
A set is a collection of well defined objects which are distinct from each other. It means that we can definitely decide whether a given particular object belongs to a given collection or not. The objects, elements and members of a set are synonymous terms.
Set are generally denoted by capital letters A, B, C, D, ……. etc. The elements of set by a, b, c, d, …… etc.
If a is an element of a set A, then we write a ∈ A and say a belongs to A.
If a does not belong to A then we write a ∉ A
Some Important Numbers Sets:
N = Set of all natural numbers
= {1, 2, 3, 4, …….}
W = Set of all whole numbers
= {0, 1, 2, 3, 4, …….}
Z or I set of all integers
= {….. -3, -2, -1, 0, 1, 2, 3, …..}
Z+ = Set of all +ve integers
= {1, 2, 3, ….} = N.
Z– =Set of all -ve integers
= {-1, -2, -3, -4, …….}
Z0= The set of all non-zero integers
={±1, ±2, ±3,…..}
Q = The set of all rational numbers.
= {p/q:p, q∈ I, q ≠ 0}
R = the set of all real numbers.
R-Q =The set of all irrational numbers.
Set Operations
There are a number of standard (common) operations which are used to manipulate sets,
producing new sets from combinations of existing sets (sometimes with entirely different
types of elements). These standard operations are:
- union
- intersection
- set difference
- symmetric set difference
- complement
- cartesian product