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:
“Ignorant kindness may have the effect of cruelty; but to be angry with it as if it were direct cruelty would be an ignorant unkindness.”
—George Eliot [Mary Ann (or Marian)
“Junk is the ideal product ... the ultimate merchandise. No sales talk necessary. The client will crawl through a sewer and beg to buy.”
—William Burroughs (b. 1914)
“Our relations to each other are oblique and casual.”
—Ralph Waldo Emerson (1803–1882)