Relations in Mathematics

Relations

Consider the following example :

                       A = { Mohan, Sohan, David, karim }  and  B = { Rita, Marry, Fatima }

Suppose Rita has two brothers Mohan and Sohan, Marry has one brother David, and Fatima

has one brother Karim. If we define a relation  R  " is a brother of "  between the elements of

A  and  B  then clearly.

Mohan R Rita , Sohan R Rita , David R Marry , Karim R Fatima.

After omitting R between two names these can be written in the form of ordered pair as:

(Mohan , Rita) , (Sohan , Rita) , (David , Marry) , (Karim , Fatima) . 

The above information can also be written in the form of a set R ordered pair as :

              R = { (Mohan , Rita) , (Sohan , Rita) , (David , Marry) , (Karim , Fatima) }

clearly   

Domain and Co-domain : 
In above example we relate  set  A  with set  B . So, the all elements of set  A  is called
Domain and the all elements of set  B  is called  Co-domain .

Range : 
In above example R is a relation between two sets  A and B  then the set of  2nd  elements
of all the ordered pairs of R is called  Range .