ABSTRACT
In chapter 3 we noted the strong similarity between the algebra of sets and that of propositions. In particular, each of the laws listed in §3.5 has a counterpart in §1.5 to which it bears more than a passing resemblance. For example, De Morgan’s laws for the propositions p and q are given by p ∨ q ≡ p¯ ∧ q¯ and p ∧ q ≡ p¯ ∨ q¯. For the sets A and B these laws take the form (A ∪B) = A¯ ∩ B¯ and (A ∩B) = A¯∪ B¯. In this chapter we shall see that the laws common to these two systems are attributable to their relationship to an algebraic structure known as a ‘Boolean algebra’ and that the properties which they share are those which are common to all Boolean algebras.
