Past exam of the mathematics course of the University of Cambridge / 2017 / ia / Paper 4 / 2D / a

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- Solution a

Solution

A binary relation on a set

S

R \subseteq S \times S

of its Cartesian product;

x R y

(x, y) \in R

. It is an equivalence relation when it is a reflexive relation, a symmetric relation, and a transitive relation:

x R x x R y ⟹ y R x x R y and y R z ⟹ x R z for every x \in S, for every x, y \in S, for every x, y, z \in S .

An equivalence relation partitions

S

into equivalence classes: two elements belong to the same class exactly when they are related.

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