PPT Slide
An algebraic structure consists of
- a set of elements B
- binary operations { + , • }
- and a unary operation { ' }
- such that the following axioms hold: 1. the set B contains at least two elements, a, b, such that a ? b 2. closure: a + b is in B a • b is in B 3. commutativity: a + b = b + a a • b = b • a 4. associativity: a + (b + c) = (a + b) + c a • (b • c) = (a • b) • c 5. identity: a + 0 = a a • 1 = a 6. distributivity: a + (b • c) = (a + b) • (a + c) a • (b + c) = (a • b) + (a • c) 7. complementarity: a + a' = 1 a • a' = 0