Compendium of Predicates
  • 🌐Orientation
    • ⭐Welcome
    • āœ’ļøNotation
    • šŸ˜…An Example
  • 🧰Definitions
    • Relation Taxonomy
    • Order Taxonomy
    • Algebra
      • Magma
      • Semigroup
      • Monoid
      • Group
      • Ringoid
      • Semiring
      • Ring
      • Unit Ring
      • Boolean Ring
      • Boolean Group
    • Bandler and Kohout Products of Relations
    • Closed
    • Complement
    • De Baets and Kerre Products of Relations
    • Extremal Elements
    • Galois Connection
    • Images of a set under a relation
    • Indexed Union and Intersection
    • Monoidal Preorder
    • Monotone Map
    • Natural Projection
    • Non-Preservation of Extrema
    • Over and Under
    • Power Set
    • Preorder
    • Preservation of Extrema
    • Product
    • Relation Inclusion
    • Row Constant Relations
    • Semilattice
    • Set Inclusion
    • Symmetric Monoidal Preorder
    • Upper Set
  • šŸ”¬Checks
    • šŸŽ™ļøA few words about the checks
    • Indirect Equality and Inclusion
    • Below
    • Extremal Elements
    • Relation Division
    • Algebra
      • Ring
      • Boolean Ring
      • Boolean Group
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  1. Definitions

Complement

Complementā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR:=⊤A,Bāˆ’R\textbf{Complement} \; A \; B \; R := \top_{A,B} - RComplementABR:=⊤A,Bā€‹āˆ’R

Relationā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Relation} \; A \; B \; RRelationABR


Notation.

  1. Complementā€…ā€ŠAā€…ā€ŠBā€…ā€ŠR\textbf{Complement} \; A \; B \; RComplementABR can be written Complementā€…ā€ŠR\textbf{Complement} \; RComplementR when AAA and BBBare clear from the context.

  2. Complementā€…ā€ŠR\textbf{Complement} \; RComplementR can be written symbolically as ¬R\neg R¬R or R‾\overline{R}R.


fun Co(A,B: set univ, R: A->B) : A->B {
  (A->B) - R
}
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Last updated 1 year ago

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