Let A and B be any two non–empty sets. Then a function ‘’ is a rule or law which associates each element of ‘A’ to a unique element of set ‘B’.
(i) A function is usually denoted by small letters, i.e. etc. and Greek letters, i.e. etc.
(ii) If ‘’ is a function from ‘A’ to ‘B’ then we write .
Let ‘a’ and ‘b’ be any two elements then an element is called an ordered pair.
Let ‘A’ and ‘B’ be any two non–empty sets, then the set of all those elements of the form, where , is called a Cartesian product.
It is denoted by
Let ‘A’ and ‘B’ be any two non–empty sets, then every sub–set of is called a binary relation from A to B.
It is denoted by ‘’i.e.
‘’ is a binary relation from A to B.
Function as a Binary Relation:
Let ‘A’ and ‘B’ be any two non–empty sets, then a binary relation ‘’ from ‘A’ to ‘B’ is called a function if it satisfied the following two conditions.
(i) Domain of , i.e.
(ii) For each element ‘x’ of ‘A’ there exists a unique element such that
Domain of a Relation:
The set of the first elements of all ordered pairs in a relation is called the domain of a relation.
Range of a Relation:
The set of the second elements of the ordered pair in a relation is called the range of a relation.
Domain of the Function:
For the set of all values of ‘x’ for which ‘y’ is finite, the definite real number is called the domain of the function.