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* The intersection of two transitive relations is always transitive. For instance, knowing that "was born before" and "has the same first name as" are transitive, one can conclude that "was born before and also has the same first name as" is also transitive.
* The intersection of two transitive relations is always transitive. For instance, knowing that "was born before" and "has the same first name as" are transitive, one can conclude that "was born before and also has the same first name as" is also transitive.
两个传递关系的交集总是可传递的。例如，我们知道“出生于...之前”的关系和“与...同名”的关系是可传递的，则可得到“既出生于...之前又与...同名”的关系也是可传递的。
两个传递关系的交集总是可传递的。例如，我们知道“出生于...之前”的关系和“与...同名”的关系是可传递的，则可得到“既出生于...之前又与...同名”的关系也是可传递的。
--[[用户:小趣木木|小趣木木]]（[[用户讨论:小趣木木|讨论]]）例如，“孔子早于孟子，孟子早于苟子，所以，孔子早于苟子。”传递关系推理是一种有效推理。如果其前提为真，那么其结论也必然真；这里的“出生于...之前”的关系和“与...同名”的关系 或许可以根据这个理解重新组织一下语言
* The union of two transitive relations need not be transitive. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. [[Herbert Hoover]] is related to [[Franklin D. Roosevelt]], which is in turn related to [[Franklin Pierce]], while Hoover is not related to Franklin Pierce.
* The union of two transitive relations need not be transitive. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. [[Herbert Hoover]] is related to [[Franklin D. Roosevelt]], which is in turn related to [[Franklin Pierce]], while Hoover is not related to Franklin Pierce.
The union of two transitive relations need not be transitive. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. Herbert Hoover is related to Franklin D. Roosevelt, which is in turn related to Franklin Pierce, while Hoover is not related to Franklin Pierce.
The union of two transitive relations need not be transitive. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. Herbert Hoover is related to Franklin D. Roosevelt, which is in turn related to Franklin Pierce, while Hoover is not related to Franklin Pierce.
=== Other properties ===<br>
=== Other properties ===<br>
==其他性质==
==其他性质==