The relation is a transitive relation if whenever a \ succeq b \; and b \ succeq c, \; then a \ succeq c \;.
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The equality of types is a reflexive, antisymmetric and transitive relation and the remaining specializations of polytypes are transitive and with this the relation \ sqsubseteq is an order.
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In mathematics, an "'equivalence relation "'is a binary relation that is at the same time a reflexive relation, a symmetric relation and a transitive relation.
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An example of a non-transitive relation with a less meaningful transitive closure is " " x " is the day of the week after " y " ".
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One example of a non-transitive relation is " city " x " can be reached via a direct flight from city " y " " on the set of all cities.
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Instead, when a broader or narrower relation is used in a triple, the corresponding transitive super-property also holds; and transitive relations can be inferred ( and queried ) using these super-properties.
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On the other hand, " is the mother of " is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.
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Another way of describing this type of parallelism is the requirement that their Playfair's axiom used in affine and Euclidean geometry is then equivalent to the statement that parallelism forms a transitive relation on the set of lines in the plane.
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"Transitive relations : where a premise based on a relation that holds between a and b and between b and c leads to the conclusion that the same relation holds between a and c, for example the causal relation is an ancestor to .
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The intersection of two transitive relations is always transitive : knowing that " was born before " and " has the same first name as " are transitive, we can conclude that " was born before and also has the same first name as " is also transitive.
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