Was asked to Work out transitive closure of:
R = {(1, 1),(1, 3),(2, 2),(2, 1),(3, 3),(4, 4),(4, 3),(4, 2)}
I did using Warshall's, getting: R*={(1,1)(1,3)(2,1)(2,2)(2,3)(3,3)(4,1)(4,2)(4,3)(4,4)}
Is R* antisymmetric?
I understand antisymmetric means if (a,b) exists and (b,a) exists then a=b.
But I am confused here, since there are symmetric elements here too: (1,2)(2,1)
Does the exclusion of (1,2)(3,1)(3,2)(1,4) etc make R* antisymmetric or symmetric or neither?
Checking element by element you see it's antisymmetric. If (2,1) and (1,2) exist, there would be a problem, but it's not the case.