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

Power Set

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Last updated 1 year ago

PowerSetā€…ā€ŠA:={ā€…ā€ŠX:XāŠ†Aā€…ā€Š}\textbf{PowerSet} \; \mathcal{A} := \{\; X : X \subseteq \mathcal{A} \; \}PowerSetA:={X:XāŠ†A}

A∈SetA \in \textbf{Set}A∈Set

AtMostā€…ā€ŠAā€…ā€ŠXā€…ā€ŠY:=Includesā€…ā€ŠXā€…ā€ŠY\textbf{AtMost} \; A \; X \; Y := \textbf{Includes} \; X \; YAtMostAXY:=IncludesXY

X∈PowerSetā€…ā€ŠAX \in \textbf{PowerSet} \; AX∈PowerSetA

Y∈PowerSetā€…ā€ŠAY \in \textbf{PowerSet} \; AY∈PowerSetA

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