Question

Consider a relation R(A,B,C,D,E,F) with functional dependencies
F =( $A\to BC$
$B\to E$
$D\to AF$
$F\to C$
$B\to AD$ )

The number of super keys present in the relation are ________

Answer 1

(a)

$A^{+}=\left\{ABCDEF\right\}$
$B^{+}=\left\{ABCDEF\right\}$
$D^{+}=\left\{ABCDEF\right\}$

Clearly, there are three candidate keys,

$Thus,N(A\cup B\cup D)=N\left(A\right)+N\left(B\right)+N\left(D\right)-\left\{N\right(A\cap B\cap D)$

$where,N(A\cap B\cap D)\text{represnts number of super}$

$\Rightarrow N(A\cup B\cup D)=3\times 2^5-3\times 2^4+2^3$

$=96-48+8=56$