Abstract
- The composite of 2 Relation -
R
and S
- Given Set
A
, B
, C
, R⊆A×B and S⊆B×C
∀x∈A,∀z∈C(xS∘Rz↔(∃y∈B(xRy∩ySz)))
- For all a in A and all z in C, the below 2 conditions must be fulfilled in order to have composition of relation S∘R
- If there is a ‘path’ from x to z, there must have a path from x to y AND y to z , the S∘R→(∃y∈B(xRy∩ySz)) part
- If there is a ‘path’ from x to y and y to z, there must has a path from x to z, the S∘R←(∃y∈B(xRy∩ySz)) part
Composition is Associative
T∘(S∘R)=(T∘S)∘R=T∘S∘R
Inverse of Composition
(S∘R)−1=R−1∘S−1