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 political mind] is a strange mixture of vanity and timidity, of an obsequious attitude at one time and a delusion of grandeur at another time. The political mind is the product of men in public life who have been twice spoiled. They have been spoiled with praise and they have been spoiled with abuse.”
—Calvin Coolidge (1872–1933)
“In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”
—Urie Bronfenbrenner (b. 1917)