distributivo

Distributivo is a term used in mathematics to describe a property of a binary operation when it interacts with another operation according to a distributive law. The most common instance is the distributive property of multiplication over addition: a*(b+c) = a*b + a*c. A similar relation holds on the right: (a+b)*c = a*c + b*c. These laws extend to subtraction as well: a*(b-c) = a*b - a*c; (a-b)*c = a*c - b*c. When an operation distributes over another from one side only, it is called left- or right-distributive, depending on which side distributes.

In other mathematical structures, the same idea appears with different operations. For example, in propositional logic, conjunction distributes over disjunction: p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r), and similarly for disjunction over conjunction in certain logics. In set theory, union distributes over intersection and intersection distributes over union: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) and A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). In algebra and lattice theory, distributive lattices are those in which the two operations ∨ and ∧ distribute over each other.

Not all operations are distributive; for example, exponentiation is not distributive over addition in the general case: a^(b+c) ≠ a^b + a^c. The distributive property is a foundational tool for simplifying expressions and proving equalities.