Posts Tagged ‘transitive’
Thursday, October 29th, 2009
Overview of Quasitransitive Relations
Description
A detailed tutorial on the property of quasitransitive relations. Step by step tutorial including several examples of quasitransitive relations for reference.
Overview
A quasitransitive relation can be mathematically defined as for all x, y, and z belonging to A, if x R y, y R z, ~(y R x), and ~(z R y), then x R z and ~(z R x). In this statement, A is a set, and R is a relation of that set. A quasitransitive relation is considered to be a weak version of a transitive relation. If the relation also happens to be asymmetric, then it is considered transitive.
Tags: arithmetic, asymmetric, negation, opposite, property, quasitransitive, r, relation, transitive, x, y, z
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Overview of Transitive Relations
Description
A detailed tutorial on the property of transitive relations. Step by step tutorial including several examples of transitive relations for reference.
Overview
A transitive relation can be mathematically defined as for all x and y belonging to A, if x R y, then y R x. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be transitive. Since a transitive relation is defined by a conditional sentence, a proof for the transitive property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, divides, empty, equal, equivalence, great, greater, implies, proof, property, r, relation, set, subset, transitive, x, y, z
Posted in Discrete Math | No Comments »
Thursday, October 29th, 2009
Introduction to Equivalence Relations
Description
A detailed tutorial on equivalence relations and how to find them. Step by step tutorial on finding equivalence relations for reference.
Overview
An equivalence relation is a relation that specifies how a set can be split into subsets. Relations can only be considered equivalence relations if they are reflexive, symmetric, or transitive. It is possible for an equivalence relation to be one of these, two of these, or all three of these, If the relation is none of them, then it is not an equivalence relation. An empty set is considered to be an equivalence relation, because it is both symmetric and transitive.
Tags: discrete math, element, empty, equivalence, reflexive, relation, set, subset, symmetric, transitive
Posted in Discrete Math | No Comments »
Tuesday, September 15th, 2009
An In-Depth Look at the Transitive Property
Description
A detailed tutorial on the use of the transitive property. Step by step tutorial including several examples of how to use the transitive property for reference.
Overview
The transitive property states that if a = b, and if b = c, then a = c. This makes sense, because the first statement, a = b, tells us that a must be the same value as b. The second statement then tells us that b = c, meaning that b and c have the same value. If c has the same value as b, and b has the same value as a, then a = c. In time the transitive property becomes something we do so often that we don\’t even think about it being an actual property anymore.
Tags: arithmetic, equals, Math, property, transitive, transitive property, values
Posted in Arithmetic | No Comments »
