## Cover set for functional dependencies - What is cover set? - What are the steps to find a cover set? - How would we say that a set of functional dependencies covers another set of functional dependencies? - Given 2 sets of functional dependencies F1 and F2, how to find F1 covers F2 or F2 covers F1? - Finding cover set of a functional dependency set

## Covers for functional dependencies

## Cover set

Given 2 sets of functional dependencies
F and G, the set of functional dependencies F is the

**of the set of functional dependencies G if every functional dependency in the set G can be inferred (derived) from the functional dependencies in the set F.***cover*

__Example 1:__
Let R (A, B, C, D, E, F) is a
relation with set of functional dependencies F = { A → BC, D → DF } and G = { A → B }.

**Does F cover G?**

If set of FDs of G can be
inferred from F, then we would say that F covers G.

The FD A → B of G can be
inferred from the FD A →
BC of F.

No more functional dependencies are
there in G. Hence,

**.**__F covers G__**Does G cover F?**

If set of FDs of F can be
inferred from G, then we would say that G covers F.

No functional dependencies of F
can be inferred from the FD A →
B of G.

Hence,

**.**__G does not cover F__

__Example 2:__
Let R (A, B, C, D, E) be a
relation with set of functional dependencies F = { A → BC, A → D, CD → E } and G = { A → BCE, A → ABD, CD → E }.

**Does F cover G?**

If set of FDs of G can be
inferred from F, then we would say that F covers G.

The FD A → BCE of G can be
inferred from the FDs A →
BC, A →
D, and CD →
E of F. [here, A gives BCD. If you know C and D then E can be derived]

The FD A → ABD of G can be
inferred from the FDs A →
BC, and A →
D of F.

The FD CD → E of G can be
inferred from the FD CD →
E of F.

All the three FDs of G can be
inferred from FDs of F. Hence,

**.**__F covers G__**Does G cover F?**

If set of FDs of F can be
inferred from G, then we would say that G covers F.

The FD A → BC of F can be
inferred from the FD A →
BCE of G.

The FD A → D of F can be
inferred from the FD A →
ABD of G.

The FD CD → E of F can be
inferred from the FD CD →
E of G.

All the three FDs of F can be
inferred from FDs of G. Hence,

**.**__G covers F__

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