What is Logic?

Logic is the basis of all mathematical reasoning and all automated reasoning. The rules of logic specify the meaning of mathematical statements. These rules help us understand and reason with statements such as –

[Tex]\exists~x~such~that~x~\neq~a^2~+~b^2,~where~\:x,~a,~b\in~Z[/Tex]

Which in Simple English means “There exists an integer that is not the sum of two squares“.

Importance of Mathematical Logic

The rules of logic give precise meaning to mathematical statements. These rules are used to distinguish between valid and invalid mathematical arguments. Apart from its importance in understanding mathematical reasoning, logic has numerous applications in Computer Science, varying from the design of digital circuits to the construction of computer programs and verification of the correctness of programs.

Propositional logic is a branch of mathematics that studies the logical relationships between propositions (or statements, sentences, assertions) taken as a whole, and connected via logical connectives.

In this article, we have covered in detail about propositional logic and related topics.