# Lecture Notes for MATH 124 - Introduction to Mathematical Thought at Boise State (BSU)

## Notes Information

 Material Type: Class Note Professor: Staff Class: MATH 124 - Introduction to Mathematical Thought Subject: Mathematics University: Boise State University Term: -- Keywords: Logical ConsequenceConsequenceAssumptionsPropositionalContinued...ContrapositiveDistinctionTraditionalInference RulesContradiction      ## Sample Document Text

M124 - Logic Lecture 5 . Analysis of arguments - Logical consequence - Rules of inference - Rules of equivalence - Formal proof of arguments Logical Consequence .Let ? be a set of formulae and f a formula - f is a logical consequence of ? if for any assignment of truth values to atomic propositions for which all of the members of ? true, f is also true -If f is a logical consequence of ?,write ??f - Note: this is consistent with ?f when f is a tautology . This is important! It is the basis of formalisation of arguments Arguments .An argument consists of: -A set ? of formulae, called the assumptions or hypotheses - A formula f, called the conclusion . If ??f then the argument is a valid argument Valid Arguments . In other words: An argument is valid if its conclusion is a logical consequence of its assumptions Notation . An intuitive way to write an argument with a set of hypotheses ? and conclusion f is as follows: ? --- ?f hypotheses conclusion Example 1 . S...

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