Sets, Relations, and Functions

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Wolfgang Schreiner
Research Institute for Symbolic Computation (RISC-Linz)
Johannes Kepler University, Linz, Austria
  • Overview
  • Motivation
  • Basics
  • Some Axioms
  • Set Enumeration
  • Subset
  • Subset and Equality
  • Subset and Equality (Continued)
  • Set Quantifier
  • Example
  • Generalized Set Quantifier
  • Example
  • Generalized Set Quantifier
  • Example
  • Logic Evaluator
  • Operational Interpretation
  • Set Union
  • Set Intersection
  • More Set Functions
  • Example
  • Set Identities
  • Set Identities
  • Proof
  • Equality Reasoning
  • Tuples
  • Example
  • Tuple Equality
  • Cartesian Product
  • Logic and Set Theory
  • Basic Idea
  • Relations
  • Relations
  • Example
  • Representation of Relations
  • Representation of Relations (Continued)
  • Representation of Relations (Continued)
  • Domain and Range
  • Example
  • Inverse of a Relation
  • Composition of Relations
  • Visualization
  • Logic Evaluator
  • Composition Laws
  • Basic Idea
  • Functions
  • Functions
  • Example
  • Example
  • Function Applications
  • Example
  • Defining Functions
  • Defining Functions
  • Example
  • Function Inversion
  • Function Composition
  • Commutative Diagrams
  • Function Composition
  • Sequences
  • Sequences
  • Example
  • Matrices
  • Example
  • Summary
    • Author: Wolfgang Schreiner
    Last Modification: October 14, 1999
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