what is composite relation .

Let A, B, and C be sets, and let R be relation from A to B and let S be a relation from B to C. Now by combining these two relations we can form a relation from A to C. Now let a belongs to A, b belongs to B, and c belongs to C. We can write relations R as a R b and S as b S c. Now by combining R and S we write a (R 0 S) c . This is called composition of Relations holding the condition that we must have a b belongs to B which can be write as a R b and b S c (as stated above) . e.g. Let A= {1,2,3,4}, B={a,b,c,d} , C ={x,y,z} and let R={ {1,a), (2, d), (3, a), (3, b), (3, d) } and S={ (b, x), (b, z), (c, y), (d, z)} Now apply that condition which is stated above (that in the composition R O S only those order pairs comes which have earlier an element is common in them e.g. from R we have (3, b) and from S we have ( b, x) .Now one relation relate 3 to b and other relates b to x and our composite relation omits that common and relates directly 3 to x.) I do not understand your second question send it again. Now R O S ={(2,z), (3,x), (3,z)}