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Homework 3: Functional Dependencies 1. Given a relation R(E,F,G,H) and the set of functional dependencies S = {E →F, EG →H, EF →G}: a. Find E + b. Is E a candidate key? Please explain your answer. 2. Given a relation R(A, B, C, G, H, I) and the set of functional dependencies S = {A → B, A → C, CG → H, CG → I, B → H} a. Find (AG)+ b. Is AG a candidate key? Please explain your answer. 3. Consider the relation schema R(A,B,C), which has the FD: B → C. If A is a candidate key for R, is it possible for R to be in BCNF? If so, under what conditions? If not, explain why not. 4. a. List all the functional dependencies that the following relation instance satisfies: b. Assume that the value of attribute Z of the last record in the relation is changed from z3 to z2. Does your list of all the functional dependencies in (a) change? 5. Suppose that we have the following three tuples in a valid instance of a relation schema R with three attributes (A,B,C): (1,6,7), (4,6,7), and (5,7,7). Specify whether each of the following FDs holds over R? (a) A → B (b) BC → A (c) B → C

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