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:
“Authority and power are two different things: power is the force by means of which you can oblige others to obey you. Authority is the right to direct and command, to be listened to or obeyed by others. Authority requests power. Power without authority is tyranny.”
—Jacques Maritain (1882–1973)
“Evil is committed without effort, naturally, fatally; goodness is always the product of some art.”
—Charles Baudelaire (1821–1867)
“What a man sows, that shall he and his relations reap.”
—Clarissa Graves (1892–1985?)