DeMorgan's theorem

    A logical theorem which states that the complement
   of a conjunction is the disjunction of the complements or
   vice versa.  In symbols:

   	not (x and y) = (not x) or (not y)
   	not (x or y)  = (not x) and (not y)

   E.g. if it is not the case that I am tall and thin then I am
   either short or fat (or both).  The theorem can be extended to
   combinations of more than two terms in the obvious way.

   The same laws also apply to sets, replacing logical complement
   with set complement, conjunction ("and") with set
   intersection, and disjunction ("or") with set union.

   A (C) programmer might use this to re-write

   	if (!foo && !bar) ...
   as
   	if (!(foo || bar)) ...

   thus saving one operator application (though an optimising
   compiler should do the same, leaving the programmer free to
   use whichever form seemed clearest).

   (1995-12-14)