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Definition: A binary relation is antisymmetric, if different elements are not mutually related.

R is antisymmetric on S : <=>
   forall x in S, y in S: (<x, y> in R /\  <y, x> in R) => x = y.

Example: the following relation is not antisymmetric:

Author: Wolfgang Schreiner
Last Modification: January 18, 2000

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