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A detailed tutorial of finding the canonical form of an object. Step by step tutorial including several examples of finding the canonical form of an object for reference.

Canonical form is also referred to as normal form or standard form. The canonical form of an object is a standard way of presenting that object. The process of finding a canonical form of something is referred to as canonization. Sometimes the word canonicalization is used instead. Canonical forms of objects are closly linked to differential forms of equations and numbers, and equivalence relations.

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A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.

Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is , where E is energy, m is the mass, and c is the speed of light in a vacuum.

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A detailed tutorial on the property of symmetric relations. Step by step tutorial including several examples of symmetric relations for reference.

A symmetric relation can be mathematically defined as for all x, y, and z belonging to A, if x R y and y R z, then x R z. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be symmetric. Since a symmetric relation is defined by a conditional sentence, a proof for the symmetric property of relations would be written as a direct proof.

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A detailed tutorial on the property of transitive relations. Step by step tutorial including several examples of transitive relations for reference.

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.

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A detailed tutorial on equivalence relations and how to find them. Step by step tutorial on finding equivalence relations for reference.

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.

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A detailed tutorial on logical equivalence. Step by step tutorial with several examples of what logical equivalence is and how to identify it for reference.

In the study of discrete math, it is said that two statements are logically equivalent if and only if their truth tables match. This means that for every possible combination of the antecedent and the consequent, these two statements must have exactly the same answer in order to be logically equivalent. There is only a true or false answer to this question, there is no “possibly” or “maybe”.