Prove that or any partition P of S, there is an equivalence relation on S whose equivalence classes are the elements of P.

Question

Prove that or any partition P of S, there is an equivalence relation on S whose equivalence classes are the elements of P.

However its converse is easy,any hints how to begin the proof. I guess i have to define a equivalence relation wisely.

Say, two elements are equivalent iff they are in the same element of the partition? — Berci, Sep 01 '19 at 16:28

mathcounterexamples.net · Accepted Answer · 2019-09-01T16:40:33.010

3

Hint

Suppose that the partition is $P= \{p_i \mid i \in I\}$.

Define $x \sim y$ if and only if $x,y$ are in the same $p_i$. Prove that this is an equivalence relation having the required properties.

edited Sep 01 '19 at 16:40

answered Sep 01 '19 at 16:30

1 Answers1