Relations Flashcards
“Alice lives in Crookes” is an example of what type of relation?
Binary relation as the number of items being related = 2.
What are binary relations?
Model relationships between a pair of objects.
What is a heterogeneous relation?
Any binary relationship between different objects or things.
What is a homogeneous relation?
A binary relation that involves elements of the same type or kind.
What is a reflexive binary relation?
A reflexive binary relation is when everything is related to itself.
What is an irreflexive binary relation?
An irreflexive binary relation is when nothing is related to itself.
What is a symmetric relation?
If for all a and b in X if a is related to b then b must be related to a.
What is an antisymmetric relation?
If there is no pair of distinct elements of X each of which is related by R to the other. If a is related to b and b is related to a then a = b.
What is an antisymmetric relation?
If for all a and b in X if a is related to b then b is not related to a.
What is a transitive relation?
If a is related to b and b is related to c then there must also be a relation from a to c.
What is a partial order relation?
A relation is partial order if it is reflexive, antisymmetric and transitive
What is a total order relation?
A total order relation is partial order and totality (where any two elements in the set can be compared)
What is equivalence relations?
A relation is an equivalence if it is reflexive symmetric and transitive.
What is a partition?
A division of a set into non-empty subsets. No element is shared between different subsets and their union is equal to the original subset.
What is a refinement?
A refinement breaks down a partition into more subsets while still maintaining the properties of a partition.
