Saturday, December 20, 2008

Types of sets

Empty set (ф)
A set is said t be empty or null or void set if it has no element and it is denoted by ф.

Singleton set
A set consisting of single element.

Finite set
A set is called a finite set if it is either void set or its elements can be listed (counted or labeled) by natural numbers 1,2,3 … and the counting of number of elements stops at a certain natural number of say (n).

The number of elements in a finite set (n) is called the cardinal number or order of a finite set A and is denoted by n(A).

Infinite set
A set who elements cannot be listed by the natural numbers however large the number may be is called an infinite set.

Equivalent set
Two finite sets are equivalent if their cardinal numbers or number of elements are same.

Equal set
Two sets A and B are equal if every element in A is a member of B and every element of B is a member of A.

When A and B are two sets, if every element of A is an element of B, then A is called a subset of B.

Universal set (U)
In discussions of sets, the superset that contains all other sets in discussion is called the universal set.

Power set
When A is a set, the collection or family of all subsets of A is called the power set of A and is denoted by P(A).

Power set is a set of subsets or elements of a power set are subsets of a set.
P(A) = {S: S is a subset of A}

If A is a finite set having n elements, the P(A) has 2n elements.

Complement of a set
If U is a universal set, the complement of a set A with respect to U is denoted as A’ or Ac or U – A . It is a set of those elements of U which are not in A.

A’ = {x| x є U, and x is does not belong to A}

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