| Allen Kent, Harold Lancour, Jay E. Daily - Language Arts & Disciplines - 1979 - 576 pages
...also true in lattices. A lattice is said to be distributive if for all elements x, y, and z in it, **x A (y V z) = (x A y) v (x A z).** It turns out that this property is equivalent to the "dual" property that x V 0> A z) = (* V y) A (*... | |
| David S. Touretzky - Computers - 1986 - 220 pages
...= x V (z A y) = x (Absorption) A distributive lattice also satisfies L5 and the equivalent L5'. L5. **x A (y V z) - (x A y) V (x A z)** (Distributive) L5'. x V (y A z) = (x V y) A (x V z) A boolean algebra is a distributive lattice satisfying... | |
| Kichoon Yang - Mathematics - 1988 - 174 pages
...Definition. Let (S, <, V, A) = S be a lattice. i) S is said to be distributive if for every x, y, z 6 S, **x A (y V z) = (x A y) V (x A z)** and x V (y A z) = (x V y) A (x V z) (the two conditions are in fact equivalent), ii) xe S is called... | |
| Vi_acheslav Nikolaevich Sali_ - Mathematics - 1988 - 113 pages
...(y V z) = (x A y) V (x A z), which is called the distributive law. Note that in any lattice we have **x A (y V z) > (x A y) V (x A z),** so that the meaning of the distributive law is really the declaration of the reverse inequality. 2.... | |
| Michael S. Paterson - Computers - 1990 - 780 pages
...automata. Recall that a Scott— domain (D,<) is distributive, if for any x,y,z 6 D such that y V z exists, **x A (y V z) = (x A y) V (x A z).** Then a dl— domain is a distributive finitary Scott-domain. Dl— domains have been much studied in... | |
| Saunders MacLane, Ieke Moerdijk - Mathematics - 1992 - 627 pages
...= x A y (or, equivalently, y = x V y). A distributive lattice L is a lattice in which the identity **x A (y V z) = (x A y) V (x A z)** (2) holds for all x, y, and z. This identity implies the dual distributive law x\I(yAz) = (xVy) A(xVz).... | |
| Roy L. Crole - Computers - 1993 - 335 pages
...aid the manipulation of meets and joins. Let X be a lattice. Then X is distributive if it satisfies **x A (y V z) = (x A y) V (x A z)** for all x, y, z in X. X is called modular if x < z implies x V (y A z) = (x V y) A z. REMARK 1.3.18... | |
| Jorge Almeida - Mathematics - 1994 - 511 pages
...(complete and) convex. A lattice is said to be distributive if the following identities are satisfied - **x A (y V z) = (x A y) V (x A z)** - x V (y A z) = (x V y) A (x V z). Exercise 1.1.4. 5how that, in the definition of distributive lattice,... | |
| Peter J. Cameron - Mathematics - 1994 - 355 pages
...lattices A lattice L is distributive if it satisfies the two distributive laws xV(yAz) = (xVy)A(xVz), **x A (y V z) = (x A y) V (x A z).** Two of our examples of lattices are distributive: the lattice P(X) of subsets of a set X , and the... | |
| Francis Borceux - Mathematics - 1994 - 443 pages
...two previous examples, one easily defines the theory of distributive lattices, by adding the axioms **x A (y V z) = (x A y) V (x A z),** x V (y A z) = (x V y) A (x V z), or the theory of boolean algebras, by adding a 1-ary operation (—... | |
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