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37 votes
37 votes

Consider the relation scheme $R = (E, F, G, H, I, J, K, L, M, N)$ and the set of functional dependencies $$\left\{ \{E, F \} \to \{G\}, \{F\} \to \{I, J\}, \{E, H\} \to \{K, L\}, \\ \{K\} \to \{M\}, \{L\} \to \{N\}\right\}$$ on $R$. What is the key for $R$?

  1. $\{E, F\}$
  2. $\{E, F, H\}$
  3. $\{E, F, H, K, L\}$
  4. $\{E\}$

4 Answers

Best answer
45 votes
45 votes
Since $E,F,H$ cannot be derived from anything else $E,F,H$ should be there in key.

Using Find $\{EFH\}^+,$ it contains all the attributes of the relation.

Hence, it is key.

Correct Answer: $B$
10 votes
10 votes

A) {EF}+ = {EFGIJ} ≠ R(The given relation)

B) {EFH}+ = {EFGHIJKLMN} = R (Correct since each member of the
                                    given relation is determined)

C) {EFHKL}+ = {EFGHIJKLMN} = R (Not correct although each member
                                of the given relation can be determined
                                but it is not minimal, since by the definition
                                of Candidate key it should be minimal Super Key)

 D) {E}+ = {E} ≠ R

3 votes
3 votes

this is my answer.

3 votes
3 votes

Any question related to functional dependencies can be solved by a simple method:

just look at the right side of all functional dependencies and note which attributes are not present at the right-hand side. Then the candidate key is definitely going to contain them because they can't be derived from the other.Now find out the closure and check the options.

If They are talking about key, they mean to say CANDIDATE KEY

for this question:- EFH is not present at right side so definitely the candidate key is going to contain them.

closure  (EFH) =  EFGHIJKLMN

So The correct option is B.

Answer:

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