A binary relation R defined on a set S is said to be transitive if, for any elements A, B, and C in the set S, given that A R B and B R C, it necessarily follows that A R C.
=== Examples of Transitive Relations ===
{| class="wikitable"
|-
! precedes
! if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times.
|-
| includes
| if A includes B, and B includes C, necessarily A includes
|}
This mathematical definition of transitivity can be
readily interpreted for many contextual relations.
A binary relation R defined on a set S is said to be transitive if, for any elements A, B, and C in the set S, given that A R B and B R C, it necessarily follows that A R C.
Examples of Transitive Relations
precedes
if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times.
includes
if A includes B, and B includes C, necessarily A includes
This mathematical definition of transitivity can be
readily interpreted for many contextual relations.