How can I prove / disprove If A ↠ BC and A → B then A → C
A,B and C are sets of attributes.


  All examples I've seen in books are like Employee ↠ Project |
  Dependent, where Employee simultaneously determines two attributes.


A ↠ B | C is a special notation different from A ↠ BC. It's useful because MVDs always come in pairs. It says that both A ↠ B and A ↠ C hold. This implies that the relation equals AB JOIN AC. Ie the relation satisfies join dependency *{AB,AC}.


  
  What does it means to have a multi valued dependency on two attributes like A ↠ BC?
  
  
  Please give an example of such a dependency.


Just think of values for subrows the way you would think of values for one attribute. Suppose {W} ↠ {X}. Then whenever W appears it's with all of some set of X values. Suppose each X has a numerator N and denominator D. Then we could have a relation {W} ↠ {N,D}. Whenever W appears it's with all of some set of &lt; N, D > subrow values.


  
  Please help me prove/disprove option C.
  
  
  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.


Hint: In my last paragraph if {W} → {N} then the variation must come from D.

Hint: If you are permitted to prove by counterexample then it's good to try to disprove things via guessing at one or more trivial examples. Eg with {W} ↠ {N,D} and {W} → {N} (A={W}, B={N}, C={D}):

  V   W   N   D
=================
| v | w | n | 1 |
-----------------
| v | w | n | 2 |
-----------------


(
How do I apply this definition of multivalued dependency (MVD) to this example relation?
)