Direct Product - Direct Product of Binary Relations

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)

    The guys who fear becoming fathers don’t understand that fathering is not something perfect men do, but something that perfects the man. The end product of child raising is not the child but the parent.
    Frank Pittman (20th century)

    Happy will that house be in which the relations are formed from character; after the highest, and not after the lowest order; the house in which character marries, and not confusion and a miscellany of unavowable motives.
    Ralph Waldo Emerson (1803–1882)