contemporary college maths logic ii euler diagrams
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Math 116LogicPart 2DefinitionsAn argument is a set of statements (called the premises) that imply another statement (called the conclusion)
Validity of an argumentAn argument is valid if the premises are all true and the conclusion is true.
An argument is invalid if all the premises are true but the conclusion is falseAnalyzing argumentsTwo methods by used to analyze arguments are by(i)Euler diagrams ( set diagrams) (ii)Truth tablesUsing Euler diagramsEuler diagrams are usually used to test the validity of an argument when the words all and some are used in the premisesUsing Euler diagramsNote the following: A and B are premisesAB None of A is in B(disjoint)
AB(Some of A is in B) Intersection
Euler diagramsA is a subset of B. All of A is in B B AExampleUse Euler diagrams to test the validity of the following:
Using truth tablesStep 1:Translate premises and conclusions into symbolic form.Step 2:Write the truth table for the premises and the conclusion.Step 3:Determine the validity of the argument. It is valid if there is a row where the premises are true and the conclusion true; Invalid if there is a row where the premises are true but the conclusion false.ExampleTest the validity of the following argument using truth tables:
SolutionTypes of Valid argumentsModus Ponens also called direct arguments is in the form
Examples of Modus Ponens
14Types of Valid arguments2. Modus Tollens also called indirect arguments is arguments in the form
Examples of Modus Tollens
16Types of Valid argumentsDisjunctive Syllogism is an argument of the form
Note : In the premise either at least one of the statements is true or maybe both OR exactly one must be true but both cannot be.
Types of Valid arguments4.Hypothetical Syllogism, also called transitivity, is an argument of the form
FallaciesA fallacy is an invalid argument form.Two common fallaciesThe fallacy of the converse.The fallacy of the inverse.21The Fallacy of the ConverseThe fallacy of the converse is the invalid argument form
This is also called the fallacy of affirming the consequent.
23Fallacy of the InverseThe fallacy of the inverse is the invalid argument form
This is also called the fallacy of denying the antecedent.