Equivalence Relationship

Equivalence Relationship

Relationship that connects elements that are similar by one of their properties.

Relationship of a set E toward a set E that is reflexive, symmetric and transitive.

  • In the case of relationships between units of measurement, it is acceptable to use the symbol =.
    However, when reading them, it is preferable to use the expression “is equal to” or “is equivalent to”.
  • So, for 1 m = 100 cm, we would say that one metre is equivalent to one hundred centimetres.


  • The relationship “…has the same parity as…” in the set of divisors of 64 is an equivalence relationship.
  • The relationship “…is parallel to…” in the set of lines on graph is an equivalence relationship.
  • The fractions  \(\dfrac{6}{9}\), \(\dfrac{10}{15}\), \(\dfrac{14}{21}\) and \(\dfrac{20}{30}\) are equivalent, because they are all equivalent to the fraction \(\dfrac{2}{3}\).
  • The units of measurement “1 m” and “100 cm” are equivalent units of measurement.
  • The relationship “…is perpendicular to…” in the set of lines on a graph is not an equivalence relationship.

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