Direct Product - Direct Product of Binary Relations

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)

    He was the product of an English public school and university. He was, moreover, a modern product of those seats of athletic exercise. He had little education and highly developed muscles—that is to say, he was no scholar, but essentially a gentleman.
    H. Seton Merriman (1862–1903)

    Words are but symbols for the relations of things to one another and to us; nowhere do they touch upon absolute truth.
    Friedrich Nietzsche (1844–1900)