In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a and b in X

if R(a,b) and R(b,a), then a = b,

or, equivalently,

if R(a,b) with a ≠ b, then R(b,a) must not hold.