No this is not true that from equivalence relations we can get partitions and from partitions we can get equivalence relations.

There is a simple reason why-

If we make a rule in which we declare that the difference between any two numbers X and Y is divisible by 2 then it is an equivalence relation.

By this Sets can be formed which can be divided into two partitions

like in set S which contains infinitely many numbers according to the rule – {0,2,4,6,8,10,12,14…..}

By this we cant partition all numbers nor get the equivalence relation back from it so we cant get partitions from equivalence relations and equivalence relations from partitions.

So the statement is false.

**PROVED**