# Translations of Encyclopedia about Mathematics

## Quantities and Logics

The concept of logics is derived from the Greek word of logos and describes the ability to apply logics to deduce results from known variables. Aristotle founded Western European logics and, starting in the 17th century, logics started to be influenced by mathematics. Formal mathematics is a tool which helps us review arguments because it studies relations between statements and the deduction of logical conclusions (proposition logics). Logical relations are actually logical connections, such "and", "or", "if–then" etc.

This is how we can determine the logical truth of a statement and how errors in thinking can be easily recognised and modified.

In 1954 in his work An Investigation of Laws of Thought, George Boole (1815-1854) described algebraic systems which use logical concepts and connections: "Boolean algebra". Using this, mathematical calculations which correspond to the laws of logics can be performed. Boolean algebra developed from the application of mathematical logics to the present logical systems, on which the operation of computers is based.

The study of sets is closely related to logics. The following theorems describe sets, or a group of people with certain characteristics and the relations between them. Here, we can speak of subsets, intersection sets and unifying sets.

"All people have a heart".

"There are some people who have only one kidney".

"No people have wings".

Diagrams are used to express something graphically and express relations between individual sets.

In logics, a trained person can use this tool to easily disprove arguments, errors and counter arguments.

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