R help - Apr 2009 - Calculate number of elements in a MECE intersection of x vectors where the total number of vectors is n

Is there a function, or code snippet that anyone is aware of that will  
give the number of elements in a MECE intersection of x vectors where  
the total number of vectors is n?

I have several vectors, A, B, C, ....,n of varying length. I am trying  
to figure out a way to systematically calculate the number of MECE  
elements in all possible combinations of 2 vectors only, then do the  
same for 3 vectors, etc.

For example, if I had just 3 vectors A, B and C, and I use the  
intersect function for each combination of 2

 > length(intersect(A,B))
 > length(intersect(A,C))
 > length(intersect(B,C))

then each result could also potentially include elements from other  
vectors as well (i.e. > length(intersect(A,B)) includes elements from  
C as well).

Any help or tips would be appreciated.

Thanks,

DMH
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