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Let $\text{R=(A,B,C,D,E)}$ having following $\text{FDs}.\;\text{F}=\{\text{A}\rightarrow \text{BC, CD} \rightarrow \text{E, B}\rightarrow \text{D, E}\rightarrow \text{A}\}.$

Which of the following is not a Candidate key?

  1. $\text{A}$
  2. $\text{B}$
  3. $\text{E}$
  4. $\text{BC}$
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In a given relation a key is a candidate key if it’s able to identify all tuples uniquely,(minimal set of attributes.

$R(A,B,C,D,E)$

$FD’S:A \rightarrow B,CD\rightarrow E,B\rightarrow D,E\rightarrow A$

clouser of $A^+=ABCDE$

clouser of $B^+=BD$

clouser of $E^+=ABCDE$

clouser of $BC^+=ABCDE$

here B is not able to identify all the tuples in the given relation. so B is not candidate key.
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