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? 


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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. 

