## Find the functional dependencies that are not holding on the given relation / Identify the wrong functional dependencies among the given / Find all valid functional dependencies of a relational table

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**Question:**

8. Let R(A, B, C, D, E, F) be a relation
with set F of functional dependencies as follows;

F = { A → B, A → C, CD → E, CD → F, B →
E }

Which of the following functional
dependencies does not hold in R?

(a) A → E

(b) CD → EF

(c) AD → F

(d) B → CD

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**Answer:**

(d) B → CD

__Discussion:__**B → CD**

B → CD is not true because the only
functional dependency that has B on left hand side is B → E. now neither E nor
B is not on the left hand side of any of the other functional dependencies.

**A → E**

A → E can be derived through the functional
dependencies A → B and B → E. [ Transitivity rule ]

**CD → EF**

CD → EF can be derived through the
functional dependencies CD → E and CD → F. [ Union rule]

**AD → F**

AD → F can be derived through the
functional dependencies A → C and CD → F. [ Pseudo-transitivity rule]