# Concept derivation guides

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Concept guide



## [Equivalence class: certify a complete finite relation first, then form classes, with a non-equivalence as contrast](/en/derivations/derivation-mko-equivalence-class-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-equivalence-class)

On X={0,1,2,3,4,5}, R is given by 12 explicitly listed ordered pairs. First certify completely that R is an equivalence relation, then compute every class from the definition [a]={x∈X ∣ aRx}; prove that aRb ⇒ [a]=[b], that any two classes are equal or disjoint and that the classes cover X, giving K(R)={{0,3},{1,4},{2,5}}. Finally use S=R∪{(0,1),(1,0)} to show that a relation failing transitivity cannot form equivalence classes.

Equivalence class

derivation-mko-equivalence-class-01





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