Generally Logic is the study of valid reasoning. But mathematical logic allows us to represent knowledge in a precise mathematical way and it also allows us to make valid inferences using a set of precise rules.

**Mathematical Logic**

George
Boole was a self-taught English Mathematician, Philosopher and Logician. His
results on **Boolean
Algebra** involving the binary numbers play an important role in
various fields, particularly more in computer applications. He introduced the
idea of Symbolic Logic and contributed a lot of results to the fast development
of Mathematical Logic.

The
reputed Greek philosopher Aristotle (384-322BC(BCE)) wrote the first book on
logic. The famous German philosopher and mathematician Gottfried Leibnitz of 17^{th}
century framed the idea of using symbols in Logic. Later this idea was realized
by George Boole and Augustus de Morgan in 19th century. George Boole
established the fact that logic is very much related to mathematics by linking
logic, symbols, and algebra together. Mathematical Logic was developed in the
late 19^{th} and early 20^{th} centuries.

In 1930
the researchers noticed (Neumann’s statement in his death bed: *0 and 1 are going to* *rule the world*) that the binary numbers
0 and 1 could be used to analyze electrical circuits and thus* *used to design electronic computers.
Today digital computers and electronic circuits are designed to implement this
binary arithmetic. We study Mathematical Logic as the language and deductive
system of Mathematics and Computer Science.

Generally Logic is the study of valid reasoning. But mathematical logic allows us to represent knowledge in a precise mathematical way and it also allows us to make valid inferences using a set of precise rules. It is regarded as a powerful tool for computer science because it is mainly used to verify the correctness of programs.

Tags : Discrete Mathematics | Mathematics , 12th Maths : UNIT 12 : Discrete Mathematics

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12th Maths : UNIT 12 : Discrete Mathematics : Mathematical Logic | Discrete Mathematics | Mathematics

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