GATE Overflow Test Series | Databases | Test 1 | Question: 16

Question

The maximum number of super keys for the relation schema $R(A_{1},A_{2},A_{3},A_{4},A_5)$ with two candidate keys $A_{1}$ and $A_{2}$ is ________

Answer 1

With $A_{1}$ as candidate key, the number of super keys, $SK(A_{1})  = 2^{4}$ (any subset of the remaining $4$ attributes including the empty set form a super key.

Similarly with $A_{2}$ as candidate key, the number of super keys, $SK(A_{2})  = 2^{4}$
    
And with $\{A_{1}A_{2}\}$ as candidate key the number of super keys, $SK(A_{1}A_{2})  = 2^{3}.$  

Now, the total number of distinct super keys $SK(A_{1}A_{2}) = SK(A_{1}) + SK(A_{2}) - SK(A_{1}A_{2})$

$\qquad = 2^{4} + 2^{4} - 2^{3} = 16 + 16 – 8 = 32 – 8 = 24.$

So, the correct answer is $24.$