Boolean algebras

  • Paul R. Halmos
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let X be an arbitrary non-empty set and let P (X) (the power set of X) be the class of all subsets of X. There is a way of introducing a Boolean structure into P (X), as follows. The distinguished elements are defined by
$$ 0 = \emptyset \:\operatorname{and} \:1 = X, $$
and, if P and Q are subsets of X, then, by definition,
$$ P + Q\left( {P \cap Q'} \right) \cup \left( {P' \cap Q} \right)\;and\;PQ = P \cap Q. $$

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

Personalised recommendations