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:

    Lesbian existence comprises both the breaking of a taboo and the rejection of a compulsory way of life. It is also a direct or indirect attack on the male right of access to women.
    Adrienne Rich (b. 1929)

    Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a classical front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.
    Eric Gill (1882–1940)

    Consciousness, we shall find, is reducible to relations between objects, and objects we shall find to be reducible to relations between different states of consciousness; and neither point of view is more nearly ultimate than the other.
    —T.S. (Thomas Stearns)