Of a transitive binary relation R. A relation R✻ defined as follows: x R✻ y iff there exists a sequence x=x0,x1,…, xn=y such that n > 0 and xiR xi+1, i=0,1,2,…, n-1 It follows from the transitivity property that if x R y then x R✻ y and that R is a subset of R✻.
x R✻ y
xiR xi+1, i=0,1,2,…, n-1
if x R y then x R✻ y
Reflexive closure is similar to transitive closure but includes the possibility that n = 0. Transitive and reflexive closures play important roles in parsing and compiling techniques and in finding paths in graphs.