# Logic And The Importance Of Logic In Mathematics

Objectives:

After completing this module, you should be able to:

1. Define Logic.

2. Appreciate the importance of Logic in mathematics.

3. Identify Propositions.

4. Convert Propositions to propositional variables.

5.

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• The term is derived from the Greek word logike – the feminine of the word logikos which means “of reason”.

• Logic then is also defined as the study of reason.

Importance of Logic

• The rules of logic specify the meaning of mathematical statements.

• Logic is the basis of all mathematical reasoning, and of all automated reasoning. It has practical applications to the design of computing machines, to the specification of systems, to artificial intelligence, to computer programming, to programming languages, and to other areas of computer science, as well as to many other fields of study.

Arguments, Premises, Conclusion

• An argument, as it occurs in logic, is a group of propositions/statements which is divided into one or more premises and one and only one conclusion.

• The statement being supported is the conclusion of the argument, and the statements that support it are the premises of the argument.

Three types of Logic

1. Propositional Logic (PL)

2. First Order Predicate Logic(FOPL)

3. Fuzzy Logic

This course will focus only in Propositional Logic.

Propositional