Boolean algebra

cosmos 19th March 2017 at 3:31am
Lattice (algebraic structure) Mathematical logic

A Boolean algebra is an Algebraic structure that models the relations between elements which can be either true or false. It is important in Mathematical logic and in Computer science.

It has the structure of an orthocomplemented, distributed Lattice (algebraic structure).

Basic rules

-----------—Main operators (Logic gates in Circuit design):

  • and
  • or
  • not
  • xor
  • nand, nor...
  • implies

Truth table, and, or, and not are a complete set for logical formulas, because can get Disjunctive normal form Boolean formulas from the any truth table.

nor is complete on its own

Disjunctive normal form

Conjunctive normal form