Some Calculations in Logic

The traditional two-valued logical calculus is concerned with propositions and their truth-values, true or false . Since the work of George Boole (1) these truth-values have been associated with the symbols 1, 0 respectively. If p denotes a proposition we use the same symbol p to denote its truth-value; thus if p is true we write p = 1 and if p is false we write p = 0. Then derived propositions such as “ not p ”, “ p and q ” have them selves truth-values which depend on those of p, q and are thus functions of the truth-values p, q .