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Introduction to Boolean algebra

Boolean algebra also known Boolean logic is a logical calculus of truth values. It is developed by George Boole. Boolean algebra resembles the real number’s algebra, but with the numeric operations of addition x + y, multiplication xy and negation −x replaced by the respective logical operations of disjunction x∨y, conjunction x∧y, and negation ¬x. Boolean operations are those and all other operations that may be built from these, for example x∧(y∨z) and these turn out to coincide with the all set of operations on the set {0,1} that take only finitely many arguments; there are total 22n such operations where there are n arguments.

Laws of Boolean algebra may be defined axiomatically by certain equations which is called axioms together with their logical consequences which is known as theorems and semantically as those equations which are true for each and every possible assignment of 0 or 1 to their variables. The axiomatic approach is complete and sound in the sense that it proves respectively neither more nor fewer laws other than the semantic approach. In short Boolean algebra is the algebra of two values. These variables are usually taken to be 0 and 1, or F and T or false and true, etc. these are also in common use.