relation doubt

Question

Number of relation S over set (0,1,2,3) such that (x,y) E S  --> x =y

Answer 1

We know :

Relation R of  a set X to Y  in general is a subset of the set of ordered pairs resulted by cartesian product of sets A and B denoted by A * B..But a relation has to satisfy a given condition..

So  here relation is defined on A --> A such that only such ordered pairs will be included which have x = y.

Hence possible ordered pairs  =   (0,0) , (1,1) , (2,2) , (3,3) ..

Now each of these can either be included or rejected hence we have 2 choices for each..

Hence number of relations   =   2 * 2 * 2 * 2

                                         =   16 [ Including null relation as in null relation , no pair hence no issue of equality , so can be considered ]