In layman’s terms:
- Reflexive: A is related to A.
- Symmetric: if A is related to B, then B is related to A.
- Transitive: if A is related to B and B is related to C then A is related to C.
In Discrete Math:
Example
Determine if ” is singing louder than” holds the properties of an equivalence relation, where the population ( set S ) is all the birds in the world that are singing in this moment in time.
- Reflexivity: is a bird singing louder than itself? No, so it is not reflexive.
- Symmetry: if bird A is singing louder than bird B, is bird B singing louder than bird A? No, so it is not symmetric.
- Transitivity: if bird A is singing louder than bird B, and bird B is singing louder than bird C, is bird A singing louder than bird C? Yes, so it is transitive.
Is “is singing louder than” an equivalence relation? No, because it is not reflexive and symmetric.