A case with Combinations in Sets

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I have two Sets A and B with N DISTINCT elements each. Both A and B
are related to each other so that B contains complement of A. For eg.A
= {a, b, c} , B = {a*, b* c*}.  I would need a perl script to generate
all possible combinations between A and B satisfying the following

a) The number of elements in the Combined set n(C) = N.
b) None of the combination should contain both an element and its
complement : i.e. {a, a*, b}, {b,c, c*} are invalid combinations.
c) There should be exactly 2^N combinations.


Re: A case with Combinations in Sets

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Since set B is completely and readily determined by set A, there is really
no point in actually having it.  Just let it be implied by A.

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So take all numbers from 0 to 2^N and map each bit-position to one of the
elements in A.  Call the ones the elements and the zeros the complements to
the elements.

foreach (0..2**$n-1) {
  print sprintf "%0$b", $_ ;


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