The Clowder Project

7.3 More Constructions With Relations

• Subsection 7.3.1: The Graph of a Function
  • Definition 7.3.1.1.1: The Graph of a Function
  • Proposition 7.3.1.1.2: Properties of Graphs of Functions
• Subsection 7.3.2: The Inverse of a Function
  • Definition 7.3.2.1.1: The Inverse of a Function
  • Proposition 7.3.2.1.2: Properties of Inverses of Functions
• Subsection 7.3.3: Representable Relations
  • Definition 7.3.3.1.1: Representable Relations
• Subsection 7.3.4: The Domain and Range of a Relation
  • Definition 7.3.4.1.1: The Domain and Range of a Relation
• Subsection 7.3.5: Binary Unions of Relations
  • Definition 7.3.5.1.1: Binary Unions of Relations
  • Proposition 7.3.5.1.2: Properties of Binary Unions of Relations
• Subsection 7.3.6: Unions of Families of Relations
  • Definition 7.3.6.1.1: The Union of a Family of Relations
  • Proposition 7.3.6.1.2: Properties of Unions of Families of Relations
• Subsection 7.3.7: Binary Intersections of Relations
  • Definition 7.3.7.1.1: Binary Intersections of Relations
  • Proposition 7.3.7.1.2: Properties of Binary Intersections of Relations
• Subsection 7.3.8: Intersections of Families of Relations
  • Definition 7.3.8.1.1: The Intersection of a Family of Relations
  • Proposition 7.3.8.1.2: Properties of Intersections of Families of Relations
• Subsection 7.3.9: Binary Products of Relations
  • Definition 7.3.9.1.1: Binary Products of Relations
  • Proposition 7.3.9.1.2: Properties of Binary Products of Relations
• Subsection 7.3.10: Products of Families of Relations
  • Definition 7.3.10.1.1: The Product of a Family of Relations
• Subsection 7.3.11: The Inverse of a Relation
  • Definition 7.3.11.1.1: The Inverse of a Relation
  • Example 7.3.11.1.2: Examples of Inverses of Relations
  • Proposition 7.3.11.1.3: Properties of Inverses of Relations
• Subsection 7.3.12: Composition of Relations
  • Definition 7.3.12.1.1: Composition of Relations
  • Example 7.3.12.1.2: Examples of Composition of Relations
  • Proposition 7.3.12.1.3: Properties of Composition of Relations
• Subsection 7.3.13: The Collage of a Relation
  • Definition 7.3.13.1.1: The Collage of a Relation
  • Proposition 7.3.13.1.2: Properties of Collages of Relations