## Composition of RelationsLet A, B, and C be sets, and let R be a relation from A to B and let S be a relation from B to C. That is, R is a subset of A × B and S is a subset of B × C. Then R and S give rise to a relation from A to C indicated by R◦S and defined by: The relation R◦S is known the composition of R and S; it is sometimes denoted simply by RS. Let R is a relation on a set A, that is, R is a relation from a set A to itself. Then R◦R, the composition of R with itself, is always represented. Also, R◦R is sometimes denoted by R
R Find the composition of relation
(i) The composition relation R
(ii) The composition relation R
## Composition of Relations and MatricesThere is another way of finding R◦S. Let M
(i) To obtain the composition of relation R and S. First multiply M The non zero entries in the matrix M Hence the composition R o S of the relation R and S is (ii) First, multiply the matrix M Hence the composition R o R of the relation R and S is (iii) Multiply the matrix M The non-zero entries in matrix M Hence the composition S o R of the relation S and R is Next TopicTypes of Relations |