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# Equivalence of functional dependencies in DBMS

## Equivalence of functional dependencies in DBMS

In this article, we will learn about the Equivalence of functional dependencies in DBMS. `Equivalence of functional dependencies`

is nothing but we need to determine whether all functional dependencies existed for the relation are equal or not.

`Equivalence of functional dependencies`

is nothing but we need to determine whether all functional dependencies existed for the relation are equal or not- You will be given a relation with different functional dependency sets of that relationship you need to check whether one functional dependency is a subset of other or both are equal.

Learn more about Functional Dependencies here on this page.

**Finding a relationship between two to FD (functional dependency) sets **

Consider S1 and S2 are two FD sets for a relation R.

, we can conclude that**If all FDs of S1 can be determined from FDs that are present in S2****S2****⊃**.**S1**, we can conclude**If all FDs of S2 can be determined from FDs that are present in S1****FD1****⊃**.**FD2**- If
then,**1 and 2 are satisfied****S1=S2.**

**Check for the equivalence of functional dependencies for A relation R (A, B, C, D) having two FD sets S1 = {A->B, B->C, AB->D} and S2= {A->B, B->C, A->C, A->D} **

**Solution: **

- Step 1. Checking whether all FDs of set S1 is present in set S2
- FD A->B in set S1 is present in set S2.
- FD B->C in set S1 is also present in set S2.
- FD AB->D in present in set S1 but not in S2 but we have to check whether we can derive it or not. In set S2, (AB) + = {A, B, C, D}. It means that A,B,C,D can be determined functionally from AB which implies AB->D holds true for set S2
- As all FDs in set S1 also hold in set S2, S2 ⊃ S1 is true.

- Step 2. Checking whether all FDs of S2 are present in S1
- FD A->B in set S2 is present in set S1.
- FD B->C in set S2 is also present in set S1.
- FD A->C is present in S2 but not in S1 but we have to check whether we can derive it or not. In set S1, (A) + = {A, B, C, D}. It means that A,B,C,D can be determined functionally from A which implies A->C holds true for set S1.
- FD A->D is present in S2 but not in S1 but we have to check whether we can derive it or not. In set S1, (A) + = {A, B, C, D}. It means that A,B,C,D can be determined functionally from A which implies A->D holds true for set S1.
- As all FDs in set S2 also hold in set S1, S1 ⊃ S2 is true.

- Step 3. We can conclude that S1=S2 as both S2⊃ S1 and S1⊃ S2 are true. Hence these two FD sets are semantically equivalent.

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