Ecm 1415 Relations Flashcards
What is the binary relation R from set A to set B?
R ⊆ A * B
R is a subset of the cartesian equation of A and B
For the relation to qualify as a function from A to B:
- For every element of the domain, there is some of the codomain Vx
- There needs to be a uniqueness x, y1, y2
What is the Cartesian product?
The product of 2 sets A and B. Writing the Cartesian product of 2 sets would entail listing every possible combination the sets hold.
What makes a binary relation?
Binary Relations leave at least one tuple that is in the cartesian product out of the relation
R = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 4)}
S = {(1, 0), (2, 0), (3, 1), (3, 2), (4, 1)}
S * R = …
S * R = {(1, 0), (1, 1), (2, 1), (2, 2), (3, 0), (3, 1)}
R = {(1, 1), (2, 1), (3, 2), (4, 3)}
R^2 = …
R^2 = {(1, 1), (2, 1), (3, 1), (4, 2)}
What are the properties a relation can have?
Reflexive
Symmetric
Antisymmetric
Transitive
What is a reflexive relation
Reflexive relation is a relation of elements of a set A such that each element of the set is related to itself
What is a symmetric relation?
According to theory, symmetry relation is the relation in which if one element is related to another element; then another element will also be related to the 1st one.
For example: In equation A, if x is only related to y, then y is also related to x for every y.
What is an antisymmetric relation?
a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other.
What is a transitive relation?
a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c
A relation on Set A is called an equivalence relation if it is…
Reflexive, Symmetric and Transitive
