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:

    ...I have never known a “movement” in the theater that did not work direct and serious harm. Indeed, I have sometimes felt that the very people associated with various “uplifting” activities in the theater are people who are astoundingly lacking in idealism.
    Minnie Maddern Fiske (1865–1932)

    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)

    Major [William] McKinley visited me. He is on a stumping tour.... I criticized the bloody-shirt course of the canvass. It seems to me to be bad “politics,” and of no use.... It is a stale issue. An increasing number of people are interested in good relations with the South.... Two ways are open to succeed in the South: 1. A division of the white voters. 2. Education of the ignorant. Bloody-shirt utterances prevent division.
    Rutherford Birchard Hayes (1822–1893)