 | Allen Kent, Harold Lancour, Jay E. Daily - 1979 - Liczba stron: 584
...V z) = (x A y) V (x A z). It turns out that this property is equivalent to the "dual" property that x V (y A z) = (x V y) A (x V z). While the lattice of subsets of a set is a distributive lattice, according to the identities of Table... | |
 | David S. Touretzky - 1986 - Liczba stron: 240
...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 L6 through L8, with a function — (complement)... | |
 | Vi_acheslav Nikolaevich Sali_ - 1988 - Liczba stron: 132
...the following identities: HI.1) xAy = yAx; 2) xVy = yVx. HII.1) x A (y V z) - (x A y) V (x A z); 2) x V (y A z) = (x V y) A (x V z), HIII.1) xAl = x; 2) xVO = x. HIV.1) xAx' = O; 2) xVx' = I. PROOF. We must show that identities WII... | |
 | Kichoon Yang - 1988 - Liczba stron: 572
...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 V-irreducible if whenever x = yVz,... | |
 | Roy L. Crole - 1993 - Liczba stron: 362
...< z then x A y < x A z and x V y < x V z (monotonicity). (vii) (x A y) V (x A z) < x A (y V 2) and x V (y A z) < (x V y) A (x V z). (viii) x < z implies x V (y A 2) < (x V y) A z. PROOF The proof is an easy application of the properties... | |
 | Francis Borceux - 1994 - Liczba stron: 470
...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 (— )* satisfying the axioms x V x*... | |
 | V.M. Kopytov, N.Ya. Medvedev - 1994 - Liczba stron: 426
...Modular Lattices. Boolean Algebras The lattice L is modular if the modular laws are fulfilled: L.6. x V (y A z) = (x V y) A (x V z) for every x, y, z 6 £, x < y. The lattices from Examples 1-3 from Section 2 are distributive. It is... | |
 | Jorge Almeida - 1994 - Liczba stron: 540
...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, it suffices to assume the validity... | |
 | David Gries, Fred B. Schneider - 1993 - Liczba stron: 536
...= 1 and thus to false . Also, the first expression below evaluates to true but the second does not. x V (y A z) = (x V y) A (x V z) p q r -,r q A -,r p V (q A -.r) t t t / / t t t f t t t t f t f f t t f f t f t f t t f f f f t f t... | |
 | Ernst W. Mayr, Claude Puech - 1995 - Liczba stron: 698
...a lattice if the supremum and the infimum of any two elements exist and distributive if furthermore x V (y A z) = (x V y) A (x V z) for any x, y, z 6 P. Then z A (y V 2) = (x A y) V (a: A *), too. Let (L, <) be a finite lattice and... | |
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L6 . x A (y V z) = (x A y) V (x A z) L6". 
