Stærðfræðimynstur í tölvunarfræði

Additional comments

More on the properties of relations

• A relation R on a set A is reflexive if (a, a) Î R for all a Î A.

• A relation R on a set A is irreflexive if (a, a) Ï R for all a Î A.

• A relation R on a set A is symmetric if [(a, b) Î R] Þ [(b, a) Î R].

• A relation R on a set A is antisymmetric if [(a, b) Î R and (b, a) Î R] Þ [a = b].

• A relation R on a set A is asymmetric if [(a, b) Î R] Þ [(b, a) Ï R].

• A relation R on a set A is transitive if [(a, b) Î R and (b, c) Î R] Þ [(a, c) Î R].

• A relation R is an equivalence relation if R is reflexive, symmetric, and transitive.

• A relation R is a partial order if R is reflexive, antisymmetric, and transitive.