Prove or disprove $\bar{A}*\overline{(B \cup C)} = \overline{(A*(B \cup C))}$ I am trying to learn Discrete mathematics by myself, from a well known book by Kenneth H. Rosen. 
I have tried to solve this problem, but, after evaluating the left side, I get stuck how to proceed with right hand side,
Here is how, I solved $\text{LHS}$ as follows: (Note : symbol $*$ is for cartesian product of sets)


$\text{let (a,x) }\epsilon \text{ } \bar{A}*\overline{(B\cup C)}$
$\Rightarrow \{(a,x)\text{ }|\text{ }x\text{ }\epsilon\ \overline{(B \cup C)} \}$
$\Rightarrow \{(a,x)\text{ }|\text{ }x\text{ }\epsilon\ {(\bar{B} \cap \bar{C})} \}$
$\Rightarrow \{(a,x)\text{ }|\text{ }x\text{ } \epsilon \bar{B} \wedge x\text{ }\epsilon\bar{C} \}$


I don't know if it's correct or not.
I solved $\text{LHS}$ using above approach, but I am not able to think of a starting point for solving the $\text{RHS}$, any suggestion or hint will help a lot.
P.S: I have just started learning discrete mathematics, so, please don't judge on asking for a naive question.

BIG HINT
Let the universal set be $\{0,1\}$ with $A=B=C=\{0\}$.
Then LHS=$\{(1,1)\}$. What is the RHS?
