1) Use Armstrong's axioms to prove the soundness of the pseudotransitivity rule.
Consider the relation schema R = (N, Y, P, M, C) and assume that the following set of functional dependencies holds on:
R: F = { N → M, NY → P, M → C}
The letters can be interpreted as follows: R = (Model_Number, Year, Price, Manufacturing_Plant, Color).
2) Evaluate each of the following as a candidate key for R, giving reasons why it can or cannot be a key: N, NY, NC.
3) Find all the candidate keys of R.
4) Show that the functional dependency NY → P does not contain extraneous attributes.
5) Show that F is already in canonical cover form.
6) Consider the decomposition d = (R1, R2) where R1 = (N, Y, P) and R2 = (N, M, C).
Is this decomposition lossless-join? Make sure to justify your answer and to show all details.