Direct Product of Binary Relations
On the Cartesian product of two sets with binary relations R and S, define (a, b) T (c, d) as a R c and b S d. If R and S are both reflexive, irreflexive, transitive, symmetric, or antisymmetric, relation T has the same property. Combining properties it follows that this also applies for being a preorder and being an equivalence relation. However, if R and S are total relations, T is in general not.
Read more about this topic: Direct Product
Famous quotes containing the words direct, product and/or relations:
“It is possible to lead astray an entire generation, to strike it blind, to drive it insane, to direct it towards a false goal. Napoleon proved this.”
—Alexander Herzen (1812–1870)
“The writer’s language is to some degree the product of his own action; he is both the historian and the agent of his own language.”
—Paul De Man (1919–1983)
“Society does not consist of individuals but expresses the sum of interrelations, the relations within which these individuals stand.”
—Karl Marx (1818–1883)