**Transitive Property of Inequalities**

Any of the following properties:

If

a<bandb<c, thena<c.

Ifa≤bandb≤c, thena≤c.

Ifa>bandb>c, thena>c.

Ifa≥bandb≥c, thena≥c.

Note: This is a property of *equality* and *inequalities*. (Click here for the transitive property of equality.) One must be cautious, however, when attempting to develop arguments using the transitive property in other settings.

Here is an example of an unsound application of the transitive property: "Team A defeated team B, and team B defeated team C. Therefore, team A will defeat team C."

**See also**

Transitive property of equality, reflexive property of equality, symmetric property of equality, inequality rules

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