We have seen that all Boolean functions can be built using only the conjunction "$\wedge$", the disjunction "$\vee$", and the negation "$\neg$" as the only connectives. This motivates the following lemma:

Lemma: Boolean Algebra of Propositional Logic

The set $B$ of all Boolean terms is a Boolean algebra $(B,\wedge,\vee,1,0)$ with respect to the conjunction "$\wedge$" and the disjunction "$\vee$".

Proofs: 1

Proofs: 1 2 3 4

Thank you to the contributors under CC BY-SA 4.0!




  1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001
  2. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982