Naive question about 3 sets intersection point

Question

I have three intersecting in at least one point sets $A$, $B$, $C$ with arbitary finite countable cardinality.

The known facts are:

$$ |A|, |B|, |C| $$ $$ |A \cap B| $$ $$ |B \cap C| $$ $$ |C \cap A| $$

Is it possible to get $|A \cap B \cap C|$ from this knowledge?

Thank you, and have a nice day!

Answer 1

Inclusion exclusion principle gives you the answer: $$|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|B\cap C|-|A\cap C|+|A\cap B\cap C|.$$ Since you have two unknown elements, you can't conclude.