Find the closure of set of attributes

How to check whether an attribute determine the other uniquely from a set of functional dependencies?, Find the closure of set of attributes, Check whether the given attributes forms candidate keys, How to find closure of attributes? Find closure - solved exercise

Question:

3. Let F = {AB → D, B → C, BC → D}. Can AC determine D uniquely?

Solution:

To find this, we need to find the closure of AC.

Closure: In simple terms, if you know an attribute (or set of attributes) in a relation R, then what other attribute (or set of attributes) you would determine uniquely is called the closure. We normally find the closure of left hand side (LHS) attributes of the functional dependencies of relation R. Closure is used to find the candidate keys of the relation. Refer here to know more about attribute closure.

To find (AC)⁺:

result := AC

We cannot move further. That is, if you know A and C you cannot determine any other attribute in the relation as per the given set of FDs. No functional dependencies in the given F contains A alone, C alone or AC together in the left hand side.

Hence, the values of attributes AC cannot determine values of attribute D uniquely.

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