Boolean algebra is a math dealing with logic which is used to design the internal workings of computer logic. It only recognizes the values 1 for true and 0 for false, - (negative sign) for not * for ”and” and + for “or”. With that and parenthesis a parallel algebra is designed complete with distributive, commutative, etc rules yet with a very reduced application and scope.
Charles Boole could have designed and implemented very different symbols to represent his math, since it is not, strictly speaking, the algebra we know. Yet, by using some of the same symbols he made it very easy for someone comfortable with traditional algebra to be able to start working very quickly with his “algebra.”