Consider the following set of functional dependencies FA which hold for relation A containing attributes A = {P,Q, R, S, T,U, V, W}:

(a) Visualize FA as a hypergraph as shown in the lecture slides [p. 608]. Make sure that the layout is not too messy and that it is clear which subsets are connected by each arrow. What do you notice? (b) Prove FAE VW → P, i.e., "every database instance that satisfies FA also satisfies VW → P" (the rhs is an implied FD), by each of the following three methods: i. Proof by using the definition of functional dependencies. ii. Proof by using the Armstrong Axioms. iii. Proof by computing the (attribute) cover {V, W }+ (p. 612f). (c) Is {V, W } a key of A? Justify your answer briefly. (d) Is {V, W } a determinant for {P,Q, R, S,T,U, V}? Explain your answer.

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