Discussion
Consider the following set of functional dipendencies of the schema (A, B, C) :
A → BC, B → C, A → B, AB → C
Then the canonical cover for this set is :
Answer: D
The canonical cover is A → B & B → C.
- Split right sides: A → B, A → C, B → C, A → B, AB → C.
- In AB → C, B is extraneous, because A → C already holds; it becomes A → C.
- A → C is redundant: it follows from A → B and B → C by transitivity.
What remains is A → B and B → C, which still implies everything in the original set. Options containing A → BC keep a redundant attribute (C is derivable from B), and AB → C has an extraneous attribute, so A, B and C are not minimal.
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