Boolean algebra, developed by George Boole in the 19th century, provides the mathematical foundation for digital computing and logical reasoning.

The fundamental operations in Boolean algebra are:

  • AND (conjunction)
  • OR (disjunction)
  • NOT (negation)

These simple operations, combined with the values True and False, form a complete system for logical reasoning. This system is not just theoretically interesting - it’s the basis for all digital computer operations, from simple calculations to complex decision-making algorithms.

De Morgan’s Laws, which show the relationship between AND, OR, and NOT operations, are particularly elegant:

  • NOT(A AND B) = (NOT A) OR (NOT B)
  • NOT(A OR B) = (NOT A) AND (NOT B)

Every time you use a computer or smartphone, you’re witnessing Boolean algebra in action!