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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. $\{E\}$
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In GO pdf answer of this question is not complete. Please fix the issue.

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: $B$
edited
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Question is about KEY. Its not mentioned that it should be a candidate key or a super key. Then how to determine what is the Answer, because option C is also a KEY coz it contains EFH too.
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if it is mentioned as key then its only candidate keys / primary key

a super key is any set of attribute that uniquely determines a tuple

whereas a key or candidate key is minimal super key

so option C is superkey. but set of attributes is not minimal

hence not a key
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Thanks a lot... :)
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With H even E & F  cannot be derived from anything else so E,F,H need to be there in key!!
+1
Really awesome way of finding keys. Must watch. Check this

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Sir EFH must be in the key
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$\{E,F,H\}$ can be determine every attributes of the relation, but $\{E,F,H\}$ cannot be determined by any other attributes,

hence, $\{E,F,H\}$ is the primary key

### D) {E}+ = {E} ≠ R

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m confused between commas in LHS part .{E,F,H} why we are taking as whole {EFH} ?
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CAN WE APPLY UNION RULE FOR COMBINING {E,F,H}
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my solution is based on given option that's why I take EFH as the combination. take a closer set of EFH you get all the attribute.
+1 vote

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.

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