We have the attributes: {A, B, C, D}.Consider the following functional dependenciesA, B, C -> DA, C -> BB -> A, C, DA, B -> C, DA -> DFind all minimal keys.
Question
We have the attributes: {A, B, C, D}. Consider the following functional dependencies
A, B, C -> D
A, C -> B
B -> A, C
DA, B -> C
DA -> D
Find all minimal keys.
Solution
To find all minimal keys, we need to follow these steps:
-
Find the closure of each attribute:
- A+ = {A, B, C, D}
- B+ = {A, B, C, D}
- C+ = {C}
- D+ = {D}
-
From the above closures, we can see that only A and B can determine all other attributes. So, we need to check if any proper subset of {A, B} can also determine all attributes.
-
The proper subsets of {A, B} are {A} and {B}. From the closures, we can see that both {A} and {B} can determine all attributes.
So, the minimal keys are {A} and {B}.
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