Mathematical Foundations·Formalization·Lesson 3 of 5

Relations and Their Properties

Defines a relation as a subset of a Cartesian product, introduces reflexivity, symmetry, transitivity, and antisymmetry, explains equivalence relations and the partitions they induce, and discusses order relations.

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In this lesson · 7 sections · 5 worked examples · 4 practice activities

A relation is a set of ordered pairs
Reflexivity and symmetry: self-loops and mirrors
Transitivity: following chains
Antisymmetry: the property that separates orders from equivalences
…and 3 more

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