/ From GATE 2007 IT:
Consider the following implications relating to functional and multi valued dependencies given below, which may or may not be correct.
A) If A ↠ B and A ↠ C then A → BC B) If A → B and A → C then A ↠ BC C) If A ↠ BC and A → B then A → C D) If A → BC and A → B then A ↠ C
Exactly how many of the above implications are valid?
A) 0 B) 1 C) 2 D) 3
I've just studied 4th Normal Form & Multi Valued Dependencies & I'm struggling to apply inference rules for multi Valued dependencies.
I've searched online though I've not found any resource on it.
If A ↠ B and A ↠ C then A → BC. This is incorrect. It is very obvious to see.
If A → B and A → C then A ↠ BC. This can be proved by using Augmentation rule of FD. A ->B & A-> C. Then we get A->BC. Using Replication rule we get ↠ BC.
If A → BC and A → B then A ↠ C. This is true, because A->BC. From which we can get A->C. From which using Replication rule we can get A ↠ C.
If A ↠ BC and A → B then A → C. Here using Coalescence rule I'm getting A->B back. I'm not able to prove/disprove A → C.
Please help me prove/disprove option C.
What does it means to have a multi valued dependency on two attributes like A ↠ BC? All examples I've seen in books are like Employee ↠ Project | Dependent, where Employee simultaneously determines two attributes. So we end up storing duplicated. But I have never encountered a multi valued dependency with two attributes on the right hand side. Please give an example of such a dependency.