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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.

Examples

  • 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  69, 1015, 1421 and 2030 are equivalent, because they are all equivalent to the fraction 23.
  • 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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