[MONOiD]

2.16 IsAntisymmetric

IsAntisymmetric( rel )

IsAntisymmetric returns true if the binary relation rel is antisymmetric and false otherwise.

    gap> IsAntisymmetric( Relation( [ [  ], [ 1 ], [ 1, 2 ] ] ) );
    true
    gap> IsAntisymmetric( Relation( [ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ] ) ) ;
    false 

A relation R subseteq {1, ..., n} x {1, ..., n} is antisymmetric if (x, y) in R and (y, x) in R implies x = y.

[Previous] [Up] [Next] 
[Index]

Version 2.4 (May 1998)

[MONOiD]