∀a,b∙aRb⟹bRa
where R is a relation. For example,
- = relation on R
- is equal to
- is married to
- {(1,2), (2,1)}
∀a,b:X∙aRb∧bRa⟹a=b
For example,
- ≤
- ≥
- ⊆
- {(1, 2), (2, 3), (1, 1)}
∀a,b:X∙aRb⟹¬(bRa)
For example,
- {(1,2), (3,4)}
∀x:X∙xRx
For example,
- =
- ≤
∀x:X∙¬(xRx)
For example,
- >, <
Coreflexive (a subset of Identity Relation)
∀x,y:X∙xRy⟹x=y)
For example,
- equal to and odd, such as {(1,1), (3,3)}
{(x,x)|x∈X}
Transitive
∀x,y,z:X∙xRy∧yRz⟹xRz
For example,
- <, =, ≤
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