2.5 Verifying Arguments Write arguments symbolically. Determine when arguments are valid or invalid. Recognize form of standard arguments. Recognize common fallacies.

We use truth tables to determine whether arguments are valid. An argument is a series of statements called premises followed by a single statement called the conclusion. An argument is valid if whenever all the premises are true, then the conclusion must also be true. The law of detachment can be written in the form [(p q) ^ p] q. The law of contraposition can be written in the form [(p q) ^ (~ q)] (~ p).

Verifying an Argument 1.Write the argument symbolically. 2.Join the premises together using the and connective. 3.Form a conditional statement using the conjunction from step 2 for the hypothesis and the conclusion of the argument as the conclusion of the conditional. 4.If the statement you form in step 3 is tautology, then the argument is valid. If there are any F’s in the final column, then the argument is not valid.

Arguments are often one of several standard forms. Valid Arguments Law of Detachment Law of Contraposition Law of Syllogism Disjunctive Syllogism p q p q p q ~ q ~ p p q q r p r p q ~ p q

Invalid Arguments Fallacy of the ConverseFallacy of the Inverse p q q p p q ~ p ~ q Keep in mind that the symbolic form, not the content, determines the validity of an argument.

Classwork/Homework Classwork – Page 120 (11 – 27 odd) Homework – Page 120 (12 – 28 even)