On the Formal Structure of the Propositional Calculus I

The prepositional calculus is the study of the set P of all elementary (or unanalysed propositions) under the three binary operations denoted by and, or, implies and the unary operation of negation. The simplest of these are probably the operations 'and', 'or' (in symbols x, +); the other two operations depend upon each other, and different views of them can be taken.