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I'm lost in the sea with the following example of decomposition without loss of dependencies...

Let be the dependencies F= {A → BC, C → AD} R is decomposed in R¹(A,B,C) & R²(A,D) I want to know if such a decomposition is without loss of dependencies and without loss of information.

I understand that it is without loss of information but why is it without loss of dependencies?

It is said so because

  • F¹={A → BC, C → A, C → B} because C → A and C → B since decomposition of A → BC. I don't understand why C → A and C → B
  • F²={A → D} but why? A → BC, C → AD therefore A → AD, no?

C → D shouldn't be lost but isn't in F¹ nor in F². Why is it important to say that?

C → A (from F¹) and A → D (from F²) therefore, C → D

The result which I don't understand at all is that it is without loss of dependencies...

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