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## 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

#### 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
(d) B → CD

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