:: For the case of binary connectives, the first, second and fourth of the five conditions above already suffice to rule out everything except NAND and NOR . The induction proofs for establishing the necessity of each of these three conditions are very simple.
12.
In brief, XLA is described in two steps : ( 1 ) give the 16 binary connectives the right geometry, the right shape value anatomy; and ( 2 ) add the transformational physiology, namely, apply the algebra of simple symmetry groups to the 16 iconic letter shape symbols.
13.
I'm in a class in which one of the problems was given that NAND and NOR have truth values that can make them complete on their own, and to prove that nand and nor are both complete on their own, AND that the other 8 binary connectives ARE NOT complete on their own.
14.
Additionally, systems of natural deduction, for example, generally require introduction and elimination rules for each connective, meaning that the use of all sixteen binary connectives would result in a highly complex NOR are sole sufficient operators, meaning that the remaining connectives can all be defined solely in terms of either of them.
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