For example I have sets
A={2,3,4}
B={3,4,5}
C={1,2,3}
for some reason I can't do AUBUC, only what i can do is calculate A, B, C.
How do I do to calculate AUBUC in this situation? is there any algorithm?
For example I have sets
for some reason I can't do AUBUC, only what i can do is calculate A, B, C. How do I do to calculate AUBUC in this situation? is there any algorithm? 

closed as too localized by Yemon Choi, Tom Leinster, Felipe Voloch, Asaf Karagila, quid Aug 22 '12 at 11:34This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


To extend the last sentence of Ilya's reply have a look in Wikipedia for the inclusionexclusion principle which accounts for the size of the intersections by the formula $$ \left A \cup B \cup C \right  = \left A \right + \left B \right + \left C \right  \left A \cap B\right  \left B \cap C \right  \left A \cap C \right + \left A \cap B \cap C\right. $$ There is an obvious generalisation to an alternating sum over the cardinalities of all the $k$fold intersections in the case of $n$ sets. Of course if you don't know the cardinalities of the intersections this is not so useful! 


I do not know, how much is it related to settheory, but from the measuretheoretical point of view, $A = \mu(A)$ where $\mu$ is a counting measure, i.e. the one which assigns the unit weight to each element of the set. In general, if you have a finite number of sets $A_1,\dots,A_n$ then $$ \mu(A_1\cup\dots\cup A_n)\leq\sum\limits_{i=1}^n\mu( A_i) $$ which is quite a trivial fact in your case. The strict inequality only holds when the sets are not disjoint, i.e. $A_i\cap A_j$ is not empty for some $i\neq j$. In that case, you have also to account for how many element are in the intersection  and to be able to compute $\mu(A_1\cap A_2)$, $\mu(A_1\cap A_2\cap A_3)$ etc. 

