Relations

binary relation

binary relation

From a set A to a set B, a subset of the Cartesian product of A and B

reflexive

(a, a) ∈ R for every element a ∈ A

symmetric

(b, a) ∈ R whenever (a, b) ∈ R, for all a, b ∈ R

antisymmetric

for all a, b ∈ A, if (a, b) ∈ R, then a = b

transitive

whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R for all a, b, c ∈ A

equivalence relation

a relation that is reflexive, symmetric, and transitive