Is the formula $A\lor (B\land C) = (A \lor B) \land (A \lor C)$ correct? I've read the formula written on the title on a mathematics' book and it doesn't seem correct for me:
For the first part of the formula [A ∨ (B∧C)] I have the following possible values:
A; B and C; A and B and C (the Or is not exclusive)
For the second part of the formula [(A ∨ B) ∧ (A ∨ C)] I have the following values:
A and A (A); A and C; B and A; B and C; ...; A and B and A and C (A and B and C)
So I can have for the second part of the formula A and B; A and C which I can't obtain with the first part of the formula.
If I'm mistaken can somebody please tell me how and give some examples.
thanks,
Bruno

Suppose you have $A \vee (B \wedge C)$.  Then you either have $A$ or $B \wedge C$.  If you have $A$, then you have $A \vee B$ and $A \vee C$.  If, on the other hand, you have $B \wedge C$, then you have both $B$ and $C$, in which case you have both $A \vee B$ and $A \vee C$.  So $A \vee (B \wedge C) \Rightarrow (A \vee B) \wedge (A \vee C)$.
Going in the other direction, suppose you have $(A \vee B) \wedge (A \vee C)$.  So you have both $A \vee B$ and $A \vee C$.  Either you have $A$, or you don't.  If you have $A$, then you have $A \vee (B \wedge C)$.  If, on the other hand, you don't have $A$, then the fact that you do have both $A \vee B$ and $A \vee C$ implies that you must have both $B$ and $C$.  Therefore you have $B \wedge C$, and so you have $A \vee (B \wedge C)$, i.e. $(A \vee B) \wedge (A \vee C) \Rightarrow A \vee (B \wedge C)$.
So we've established that $A \vee (B \wedge C) \Rightarrow (A \vee B) \wedge (A \vee C)$ and $(A \vee B) \wedge (A \vee C) \Rightarrow A \vee (B \wedge C)$.  Therefore $A \vee (B \wedge C) = (A \vee B) \wedge (A \vee C)$.
