Asymmetric Relation

A relation ‘R’ is said to be antisymmetric if xRy then !(yRx) ∀x,y∈A If (x,y)∈R then (y,x)∉R ∀x,y∈A

That means R contains elements of the form (c,d) but must not contain (d,c)

Example #

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

• R is not symmetric: does not contain (2,2),(3,3)
• R is antisymmetric: does not contain (2,1),(3,1) for the elements corresponding to (1,2),(1,3)
• R is not asymmetric: contains (1,1)

Note #

Every Asymmetric is Antisymmetric.