Reflexive Relations:
R is a reflexive relation if (a, a) € R, a € A. It could be noticed if there is at least one member a € A like (a, a) € R, then R is not reflexive.
Symmetric Relations:
R is called a symmetric relation on A if (x, y)€ R →(y, x) € R
That is, y R x when x R y.
It could be noticed that R is symmetric iff R-1 = R
Assume A = {1, 2, 3}, then R = {(1, 1), (1, 3), (3, 1)} is symmetric.
Anti-symmetric Relations:
R is called as a anti-symmetric relation if (a, b) €R and (b, a) €R →a = b
Thus, if a € b then a can be belongs to b or b can be belongs to a, but never both.
Or, we have never both a R b and b R a apart from when a = b.