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Sets


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 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