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databasefunctional-dependencies

derivation of nontrivial dependencies

I am seeking for help. I am stuck over a question based on functional dependency.

Consider the relation schema R= (A, B, C, D, E, G) and the set F of functional dependencies: A → BC BD → E CD → AB a. Derive the nontrivial dependencies from F using Armstrong’s axioms: AD → E and CD → E. Show all steps.

I can not understand the question. As per my understanding, here all functional dependencies are non trivial. So what is the meaning of Armstrong’s axioms: AD → E and CD → E.

Also, what is the meaning of derivation of nontrivial dependencies?

Solution

  • Let’s try to derive AD → E from the Armstrong’s axioms (I think this is the request of the exercise).

    Here are the steps of derivation:

    1. A → BC (given)
2. BD → E (given)
3. AD → BCD (for augmentation from 1)
4. BCD → BD (for reflexivity)
5. AD → BD (for transitivity from 3 and 4)
6. AD → E (for transitivity from 5 and 2)

    I left the derivation of CD → E as exercise.