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)
“...In the past, as now, [Hollywood] was a stamping ground for tastelessness, violence, and hyperbole, but once upon a time it turned out a product which sweetened the flavor of life all over the world.”
—Anita Loos (1888–1981)
“Society does not consist of individuals but expresses the sum of interrelations, the relations within which these individuals stand.”
—Karl Marx (1818–1883)