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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra. For example, in elementary arithmetic , one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).}
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
An element x is called a dual distributive element if ∀y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z). In a distributive lattice, every element is of course both distributive and dual distributive. In a non-distributive lattice, there may be elements that are distributive, but not dual distributive (and vice versa).
Distribution law or the Nernst's distribution law [1] [2] [better source needed] gives a generalisation which governs the distribution of a solute between two immiscible solvents. This law was first given by Nernst who studied the distribution of several solutes between different appropriate pairs of solvents.
Distributivity, a property of binary operations that generalises the distributive law from elementary algebra; Distribution (number theory) Distribution problems, a common type of problems in combinatorics where the goal is to enumerate the number of possible distributions of m objects to n recipients, subject to various conditions; see ...
The principle of distributivity states that the algebraic distributive law is valid, where both logical conjunction and logical disjunction are distributive over each other so that for any propositions A, B and C the equivalences
In his book A Theory of Justice, John Rawls outlines his famous theory about justice as fairness. The theory consists of three core components: [4] the equality of people in rights and liberties; the equality of opportunities for all; and; an arrangement of economic inequalities focused on benefit maximisation for those who are least advantaged.