For understanding the equivalence of Functional Dependencies Sets (FD sets), the basic idea about Attribute Closuresis given in this article Given a Relation with different FD sets for that relation, we have to find out whether one FD set is a subset of another or both are equal.

 How do find the relationship between two FD sets? Let FD1 and FD2 be two FD sets for a relation R.

If all FDs of FD1 can be derived from FDs present in FD2, we can say that FD2 ⊃ FD1.
If all FDs of FD2 can be derived from FDs present in FD1, we can say that FD1 ⊃ FD2.
If 1 and 2 both are true, FD1=FD2.

Suppose in the designing process we convert the ER diagram to a relational model and this task is given to two different engineers. Now those two engineers give two different sets of functional dependencies. 

So, being an administrator we need to ensure that we must have a good set of Functional Dependencies. To ensure this we require to study the equivalence of Functional Dependencies.

Equivalence of Functional Dependencies: https://www.geeksforgeeks.org/equivalence-of-functional-dependencies-sets/