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) Function is usually denoted by small letters i.e. etc and the Greek letter 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 elementis called 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 Cartesian product.
It is denoted by
Let ‘A’ and ‘B’ be any two non–empty sets, then every sub–set of is called 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 iff it satisfied the following two conditions.
(i) Domain of , i.e.
(ii) For each element ‘x’ of ‘A’ there exist a unique element such that
Domain of a Relation:
The set of the first elements of all ordered pair in a relation is called, domain of a relation.
Range of a Relation:
The set of the second elements of the ordered pair in a relation is called, range of a relation.
Domain of the Function:
The set of all those values of ‘x’ for which ‘y’ is finite, definite real number is called domain of the function.