Find the functional dependency that is not hold in a relation

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

(c) AD → F

(d) B → CD

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]

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