Monday, December 22, 2008

Composites

A composite is a way of relating 3 or more sets.

Let R be a relation from A to B, and let S be a relation from B to C. The composite of R and S is: There is exists a b in B such that (a,b) is in R and (b,c) is in S.

Consider the example:

A={1,2,3,4}
B={1,2,3,4}
C={1,2,3,4}

Let R be a relation from A to B, so

R = {(1,p),(1,q),(2,q),(3,r),(4,s)}

and let S be the relation from B to C:

S = {(p,x),(q,x),(q,y),(s,z)}

Thus the composite of S and R can be seen as the relation of A to C via B.

The composite of S and R = {(1,x),(1,y),(2,x),(2,y),(4,z)}

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