Boolean Algebra: The Mathematics of True and False
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!