Transitive Relations
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Mathematical Definition
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.