# 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  $$\dfrac{6}{9}$$, $$\dfrac{10}{15}$$, $$\dfrac{14}{21}$$ 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.