Question

Consider a relation R(A, B, C, D, E) with functional dependencies
$F=\{A\to B,BC\to E,ED\to A\}$
Number of additional relations required to convert it into lossless, dependency preserving 3NF decomposition__________

Answer 1

$\text{Relation R(A, B, C, D, E)}\begin{array}{cc}F& =\{A\to B,BC\to E,ED\to A\}\\ {\text{Closure of (CDE)}}^{+}& =\left\{ABCDE\right\}\\ \text{So CDE is a candidate key of R}& \\ {\text{Closure of (ACD)}}^{+}& =\left\{ABCDE\right\}\\ \text{ACD is a candidate key of R}& \\ {\text{Closure of (BCD)}}^{+}& =\left\{ABCDE\right\}\\ \text{BCD is a candidate key of R}& \\ \text{Total 3 key CDE, ACD, BCD}& \\ & \end{array}$
$\text{A, B, C,D, E all are key attribute so relation R is already is 3NF, So no additional relation}\text{required.}$