For a basic introduction to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic.
For an alternative perspective see Boolean algebras canonically defined.
In abstract algebra, a Boolean algebra is an algebraic structure (a collection of elements and operations on them obeying defining axioms) that captures essential properties of both set operations and logic operations. Specifically, it deals with the set operations of intersection, union, complement; and the logic operations of AND, OR, NOT.
For example, the logical assertion that a statement a and its negation ¬a cannot both be true.
