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Boolean Algebra

In the field of mathematics and in mathematical logic, Boolean algebra is defined as the branch of algebra where the values of the variables are the truth values ‘true’ and ‘false’, typically denoted by 1 and 0, respectively. Instead of elementary algebra, where numbers are the values of the variables and the prime operations are multiplication and addition, the main operations of this algebra are:

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  • The conjunction denoted as ‘∧’
  • The disjunction denoted as ‘∨’
  • The negation denoted as ‘¬’

It is hence a formalism that is used to describe logical operations in the same way that elementary algebra was used to describe numerical operations. Boolean algebra, as a concept, was introduced by George Boole in his first book ‘The Mathematical Analysis of Logic’, which was cemented by his next book, ‘An Investigation of the Laws of Thought’. As per Huntington, the term Boolean algebra was initially suggested by Sheffer in 1913, although Charles Sanders Peirce later gave the title “A Boolean Algebra with One Constant’ to the first chapter of his ‘The Simplest Mathematics’ in the year 1880. Boolean algebra has been fundamental in developing digital electronics and is provided for in all modern programming languages. It is also used in statistics and set theory.

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