Final answer:
Properties of Boolean algebra include the associative, commutative, and distributive properties, which dictate how variables can be grouped, ordered, and distributed in logical operations. Boolean algebra also relies on fundamental postulates like complementarity, identity, and duality, which form the foundation of how the algebraic system operates.
Step-by-step explanation:
The properties and postulates of Boolean algebra include the associative, commutative, and distributive properties. The associative property means that the grouping of variables does not affect the outcome of logical operations: (A+B)+C = A+(B+C) for OR operations and (AB)C = A(BC) for AND operations. The commutative property indicates that the order of variables does not change the result: A+B = B+A and AB = BA. The distributive property allows for each factor to be distributed across terms combined by the other operation: A(B+C) = AB+AC.
Additionally, Boolean algebra is based on a set of fundamental postulates that define how the algebraic system operates. These postulates are assumed to be true without proof and they are used to deduce other truths within the system. In Boolean algebra, these include principles such as complementarity (every element has a complement), identity (0 and 1 serve as identities for OR and AND operations, respectively), and duality (every Boolean equation remains valid if operators and identities are swapped).Boolean algebra is a mathematical structure used in logic and computer science to analyze and simplify logical expressions. The properties, such as commutative, associative, distributive, identity, and negation, help manipulate and simplify Boolean expressions. These postulates are based on the properties of logical propositions and allow us to evaluate the truth value of statements.