## Logical Foundations: Mathematical Reasoning

Aristotle was one of the earliest writers on Logic. However, George Boole, was the first one to apply mathematical methods in Logic. Hence the study of Logic is also called Boolean Logic.

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You'll start with the basic definition of a statement and how to identify one.If a statement is true, it's truth value is T, if it is false, it's truth value is F. You'll also learn what is negation of a statement and how to write one. Next, you learn about Compound statements and how to connect them using Conjunction and Disjunction.

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You learn about Quantifiers. There are two types of Quantifiers, there exists and for all. Also learn how to negate a Quantified statement.

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Then you have the Conditional and Biconditional statements. You'll learn how to construct truth tables for Conjunction, Disjunction, Implication and Bi conditional. This is followed by learning how to construct the Converse, Inverse and Contrapositive of a statement.

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An easy method to do this would be to break each statement into its symbolic form, construct the converse, inverse and contrapositive and then convert it into statements. As you construct truth tables, you'll also learn to determine whether a given statement is a Tautology or a Contradiction.

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We conclude this lesson by learning how to validate statements. This can be done by three methods, direct method, method of contrapositive and contradiction method.

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