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A relation R over AxB is asymmetric if for at least one (a,b), there is no (b,a).

Examples

R is a relation over A (this means R is a subset of AxA)

$A={1,2,3}$

$R={(1,2),(2,1),(1,3)}$

R is asymmetric because there is no (3,1) for (1,3) in R.