Equivalence Class

Equivalence Class

Each subset induced in a set by a relation of equivalence defined in this set.

Examples

  • The relation of congruence modulo n in the set of integers is a relation of equivalence.
  • If we group together the elements of E ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10} based on the relation R: … has the same remainder as… when we divide by 3, we get three equivalence classes: {1, 4, 7, 10}, {2, 5, 8} and {3, 6, 9}.
  • Consider the set of integers that are less than 4 and greater than -4.
    Consider the equivalence relation R: … has the same value as … as absolute value.
    We get these 4 equivalence classes: {-3, 3}, {-2, 2}, {-1, 1}, {0}.

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