distributivity's Usage Examples:

is commutative, then left-distributivity implies right-distributivity and vice versa, and one talks simply of distributivity.

of order theory, there are various notions of the common concept of distributivity, applied to the formation of suprema and infima.

Complete distributivity is a self-dual property, i.

matrices of respective sizes m × n, n × p, n × p, and p × q, one has (left distributivity) A ( B + C ) = A B + A C , {\displaystyle \mathbf {A} (\mathbf {B} +\mathbf.

from those of classical propositional logic in that the principle of distributivity fails.

The principle of distributivity states that the algebraic distributive law is valid for classical logic, where both logical conjunction and logical disjunction.

relationship of this condition to other distributivity conditions of order theory can be found in the article on distributivity (order theory).

space is commutative, left distributivity and right distributivity are equivalent, and, in this case, only one distributivity requires a proof.

eliminativity and distributivity.

normal form or disjunctive normal form by applying distributivity.

Repeated application of distributivity may exponentially increase the size of a formula.

(x+1)^{2}-(x-1)^{2}} , one can put it in standard form by expanding the products (by distributivity) and combining the like terms; for example, ( x + 1 ) 2 − ( x − 1 ).

seen from these examples, familiar properties like associativity and distributivity may fail in saturation arithmetic.

Surprisingly, there is a notion of "distributivity" applicable to semilattices, even though distributivity conventionally requires the interaction.

In a similar way, one sees that the infinite distributivity law x ∧ ⋁ S = ⋁ { x ∧ s ∣ s ∈ S } {\displaystyle x\wedge \bigvee S=\bigvee.

incorrect: (x + y)2 can be correctly computed as x2 + 2xy + y2 using distributivity (commonly known as the FOIL method).