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A report if equivalence is reflexive, symmetric and transitive.
attimino a repeat for those who have forgotten elder properties of mathematical relationships, a relation R is algebraic:



reflexive: if every element of the environment in relation to himself antiglare if nothing is in relation to himself

symmetric: if reversing the order of variables, the relationship is always true (for all items)

antisymmetric: if reversing the order, the relationship is not never true (for all items)

transitive: if a triple x, y and z, x is related to y, z y, z EX with
clear now the concept, we move to the point.
An equivalence relation organizes the elements of a set or sets in other groups, which are called equivalence classes
. The set has all the elements for a set of equivalence classes, takes the quotient set
name. All items (subset of the environment) of the whole quotient with the following properties:

are disjoint in pairs (the union of two sets gives us the empty set)
Nobody is empty (Each set has at least one element)
Their union gives the set environment (Each element of the environment is contained in some equivalence class)
So we can say that the quotient set is a partition
whole environment.

Examples of equivalence relations: 1) In a school we have 800 students and 5 classes or sections Modules include: A, B, C, D, E. The first 120 are in A, B during the next 170, another 150 in Section C, 260 in D, 200 in E. It is clear that each section / course contains a number of distinguished students from other courses, that every student can attend only one course (For this we say that the sets are disjoint, because they do not contain elements in common), and no part is without students Finally, no student is out of the following courses. If the union of the sections gives us a whole institution, then we have used an equivalence relation. 2) In a 24 carabinieri barracks, we know that each police officer has a certain degree. The ranks of the police are mere policeman, police officer chosen, pinned sergeant and sergeant. To form the barracks, each degree must contain at least one officer, and every officer must belong to one degree between them. The union of the officers of all ranks, as a result gives us the set of all elements of the police station or barracks.