Endorelation/Examples

Examples of Endorelation

Arbitrary Relation

Let $V_0 = \set {a, b, c}$.

A possible endorelation on $V_0$ is:

$R = \set {\tuple {a, a}, \tuple {b, b}, \tuple {b, c}, \tuple {c, b} }$

Properties of Arbitrary Relation: 1

Let $V = \set {u, v, w, x}$.

Let $E$ be the relation on $V$ defined as:

$E = \set {\tuple {u, v}, \tuple {v, u}, \tuple {v, w}, \tuple {w, v} }$

Then $E$ is:

antireflexive
symmetric
non-transitive.

Properties of Arbitrary Relation: 2

Let $V = \set {a, b, c, d}$.

Let $R$ be the relation on $V$ defined as:

$E = \set {\tuple {a, a}, \tuple {a, b}, \tuple {a, c}, \tuple {a, d}, \tuple {b, b}, \tuple {b, c}, \tuple {b, d}, \tuple {c, c}, \tuple {c, d}, \tuple {d, d} }$

Then $E$ is:

reflexive
antisymmetric
transitive.

Properties of Arbitrary Relation: 3

Let $V = \set {a, b, c, d}$.

Let $R$ be the relation on $V$ defined as:

$r = \set {\tuple {a, a}, \tuple {a, b}, \tuple {b, b}, \tuple {b, c}, \tuple {c, b}, \tuple {c, c} }$

Then $E$ is:

non-reflexive
non-symmetric
non-transitive.