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:
“Bryan is the least of a liar I know in public life. I have always found him direct and honest, and he never goes back on what he has said to me in private—a rare thing, if found, in public men. I found him purely frank.”
—William Howard Taft (1857–1930)
“Good is a product of the ethical and spiritual artistry of individuals; it cannot be mass-produced.”
—Aldous Huxley (1894–1963)
“Children, who play life, discern its true law and relations more clearly than men, who fail to live it worthily, but who think that they are wiser by experience, that is, by failure.”
—Henry David Thoreau (1817–1862)