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
R
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
included in
is less than
is greater than
supports
implies
causes
The generic phrase 'is subordinate to' can be used to represent any of the above relations.
This mathematical definition of transitivity can be
readily interpreted for many contextual relations.