Algebraic Properties Definitions

Supplementary to Dale & Lewis Chapter 4

• com·mu·ta·tive
  
  1. Relating to, involving, or characterized by substitution,
  interchange, or exchange.
  2. Independent of order. Used of a logical or mathematical operation
  that combines objects or sets of objects two at a time. If a × b = b ×
  a, the operation indicated by × is commutative.
  
  
  
• as·so·ci·a·tive
  
  1. Of, characterized by, resulting from, or causing association.
  2. Mathematics. Independent of the grouping of elements. For example, if
  a + (b + c) = (a + b) + c, the operation indicated by + is associative.
  
  
  
• dis·trib·u·tive
  
  1. a. Of, relating to, or involving distribution. b. Serving to distribute.
  2. Mathematics. Of or relating to a rule that the same product results
  in multiplication when performed on a set of numbers as when performed
  on members of the set individually. If a × (b + c) = a × b + a × c, then
  × is distributive over +.
  
  
  
• i·den·ti·ty
  
  1. The quality or condition of being the same as something else.
  2. Mathematics.
  a. An equation that is satisfied by any number that replaces the letter
  for which the equation is defined.
  b. Identity element.
  
  
• com·ple·ment
  
  1. Either of two parts that complete the whole or mutually complete each
  other.
  2. Mathematics & Logic. For a universal set, the set of all elements in
  the set that are not in a specified subset.
  
  
• DeMorgan’s Law: See Dale and Lewis, p. 108