Who Invented Boolean Algebra. One of Boole’s most significant contributions to mathematics was the development of Boolean algebra. He published his most famous work, “The Mathematical Analysis of Logic,” in 1847, where he introduced symbolic logic and Boolean algebra.
Who Invented Boolean Algebra.
This form of calculation developed by George Boole is a system by which certain logical reasoning can be expressed in mathematical terms. The elements of Boolean algebra are a set of propositions, that is, facts expressed by natural language sentences.
Such propositions have the property of being true or false. At the same time, and regardless of whether they are true or false, each proposition has what is called its complementary proposition, which is nothing but its negation: the negation of the proposition P is the complementary proposition P ‘ .
The consequences of these propositions can be discovered by performing mathematical operations on the symbols that represent them. The two basic operations are conjunction and disjunction. Its meaning is easy to understand if one thinks of the two corresponding grammatical particles, the copulative conjunction “and” (with the idea of addition or addition) and the disjunctive conjunction “or” (with the idea of exclusion). In natural language, however, such conjunctions can have other values, which is obviously not the case in Boolean algebra.
As a simple example, consider the following two propositions: “I will be home today” and “I will be home tomorrow”. We represent the first proposition with the symbol P and the second with the symbol Q. The two propositions can be combined in one of two ways: on the one hand, P or Q (I will be home today or I will be home tomorrow), and, on the other hand, P and Q (I will be home today and I will be home tomorrow).
The rules of Boolean algebra can be used to determine the consequences of various combinations of these propositions depending on whether the propositions are true (T) or false (F). Thus, if both propositions are true, the combination P and Q is also true. That is, if the proposition “today I will be at home” ( P ) is true, and the proposition “tomorrow I will be at home” ( Q ) is also true, then the combination “today I will be at home and tomorrow I will be at home” ( P and Q ) must also be true.
Suppose instead that P is true and Q is false. That is, the proposition “today I will be at home” ( P ) is true, but the proposition “tomorrow I will be at home” ( Q ) is false. In such a case, the combination “I’ll be home today and I’ll be home tomorrow” ( P and Q ) must be false. As you can imagine, most of the questions that Boolean algebra addresses are much more difficult than this simple example. Over time, mathematicians have developed complex techniques to formalize and calculate very complicated logical processes.
Two elements of Boolean algebra make it a very important mathematical form for practical application. First, propositions expressed in everyday language (such as “I’ll be home today”) can be turned into mathematical expressions, such as letters and numbers. Second, those symbols generally have one of two values: the propositions can be affirmative or negative (complementary); the operations are conjunction or disjunction; and not only the propositions, but also the result of their combinations ( P , Q , P and Q , P or Q ), are true or false. This means that they can be expressed by means of a binary system: true or false; yes or no; 0 or 1.
