Discrete Math - 9.1 Relations and Properties & 9.5 Equivalence Relations

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Relation

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A relation R from the set A to the set B is a subset of AxB.

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Reflexive

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∀a∈A (a, a)∈R

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8 Terms

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Relation

A relation R from the set A to the set B is a subset of AxB.

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Reflexive

∀a∈A (a, a)∈R

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Symmetric

∀a, b∈A (a, b)∈R ⟹ (b, a)∈R

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Antisymmetric

∀a, b∈A [(a, b)∈R ∧ (b, a)∈R] ⟹ a = b

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Transitive

∀a,b,c∈A [(a, b)∈R ∧ (b, c)∈R] ⟹ (a, c)∈R

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Equivalence relation

R is reflexive, symmetric, and transitive

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Equivalence class

the set of all elements of A to which a is related by R

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Representative

if b∈[a]R, then b is the representative of this equivalence class