Use Armstrong's axioms to prove the soundness of the pseudotransitivity rule. II. 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).
Evaluate each of the following as a candidate key for R, giving reasons why it can or cannot be a key: N, NY, NC.
Find all the candidate keys of R.
Show that the functional dependency NY → P does not contain extraneous attributes.
Show that F is already in canonical cover form.
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.