An equivalence relation is a special type of relationship between elements in a set that satisfies three key properties: reflexivity, symmetry, and transitivity. Reflexivity means that every element is related to itself. Symmetry indicates that if one element is related to another, then the second element is also related to the first. Transitivity states that if one element is related to a second, and that second element is related to a third, then the first element is also related to the third. These properties allow us to group elements into equivalence classes, where each class contains elements that are all related to each other. For example, in the set of integers, the relation of congruence modulo n forms an equivalence relation, where integers are considered equivalent if they have the same remainder when divided by n. This concept is fundamental in various areas of mathematics, including set theory and abstract algebra.