Given $|A\cap B|$, $|A\cap C|$ and $|B\cap C|$, what is $|A\cap (B\cap C)|=$?

Question

Suppose we know about $A\\cap B$, $A\\cap C$, and $B\\cap C$. Here, each set is a binary representation of a decimal number, hence each set includes 0\'s and 1\'s with speci