edited by
13,367 views
26 votes
26 votes

Consider a relation scheme $R = (A, B, C, D, E, H)$ on which the following functional dependencies hold: {$A \rightarrow B$, $BC \rightarrow D$, $E \rightarrow C$, $D \rightarrow A$}. What are the candidate keys R?

  1. $\text{AE, BE}$
  2. $\text{AE, BE, DE}$
  3. $\text{AEH, BEH, BCH}$
  4. $\text{AEH, BEH, DEH}$
edited by

3 Answers

Best answer
38 votes
38 votes
(d) AEH, BEH, DEH

using the given functional dependencies and looking at the dependent attributes, E and H are not dependent on any. So, they must be part of any candidate key. So, only option is D. If we see the FD's, adding A, B or D to EH do form candidate keys.
selected by
8 votes
8 votes

Answer :  OPTION D
You can directly find the candidate key using two rules or you can say necessary attributes. 
An Attribute A is said to be a necessary attribute if 

(a)  A occurs only in L.H.S. (left hand side ) of the FD's(functional dependencies) in F  and/or
 
(b)  A is an Attribute in relation, But A doses not occur either in L.H.S. or R.H.S. of any FD in F. 

In other words, Necessary attributes never occur in the RHS of any FD in F. 

Here we can directly see, both attribute E and H not occur in RHS of any FDs. So, both of are necessary part of a candidate key. 
 

0 votes
0 votes
(D)
A set of attributes S is candidate key of relation R if the closure of S is all attributes of R and there is no subset of S whose closure is all attributes of R.
Closure of AEH, i.e. AEH+ = {ABCDEH}
Closure of BEH, i.e. BEH+ = {ABCDEH}
Closure of DEH, i.e. DEH+ = {ABCDEH}
Answer:

Related questions

24 votes
24 votes
3 answers
3
Kathleen asked Sep 22, 2014
15,034 views
Consider a direct mapped cache of size $32$ $KB$ with block size $32$ $bytes$. The $CPU$ generates $32$ $bit$ addresses. The number of bits needed for cache indexing and ...
27 votes
27 votes
1 answer
4
Kathleen asked Sep 22, 2014
6,753 views
Match each of the high level language statements given on the left hand side with the most natural addressing mode from those listed on the right hand side.$$\begin{array...