Reflexive Relation/Examples
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Examples of Reflexive Relations
Arbitrary Reflexive Relation
Let $V_0 = \set {a, b, c}$.
A reflexive relation on $V_0$ must include the ordered pairs:
- $\tuple {a, a}, \tuple {b, b}, \tuple {c, c}$
Reflexive Relation on Cartesian Plane
The subset of the Cartesian plane defined as:
- $\RR := \set {\tuple {x, y} \in \R^2: x \le y \le x + 1}$
determines a relation on $\R^2$ which is reflexive, but neither symmetric nor transitive.
Distance Less than 1
Let $\sim$ be the relation on the set of real numbers $\R$ defined as:
- $x \sim y \iff \size {x - y} < 1$
Then $\sim$ is reflexive and symmetric, but not transitive.