Search⌘ K
AI Features
Home
Courses
An Introduction to Basic Set Theory

Equivalence Relations

Explore equivalence relations in set theory by understanding their defining properties: reflexivity, symmetry, and transitivity. This lesson uses practical examples like parallelism, congruence modulo, and triangle similarity to illustrate the concept and includes Python code to test these properties in relations.

We'll cover the following...

Equivalence relation

A relation RR is an equivalence relation on set AA if it has the following three properties:

  • RR is reflexive, that is, for every element aa of AA, we have (a,a)(a,a) in RR.

  • RR is symmetric, that is, if (a,b)(a,b) is in RR, then (b,a)(b,a) is also in RR.

  • RR is transitive, that is, if (a,b)(a,b) and (b,c)(b,c) are in RR ...