Math Problem Statement

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table​ or, if​ applicable, compare the​ argument's symbolic form to a standard valid or invalid form.​ (You can ignore differences in​ past, present, and future​ tense.) If he tries hard​, he will do poorly. He will do well. He does not try hard. Let p be the statement ​"he tries hard​," and q be the statement ​"he will do well​." Select the correct answer below and fill in the answer box to complete your choice. ​(Type the terms of your expression in the same order as they appear in the original​ expression.) A. The argument is valid. In symbolic​ form, the argument is    enter your response here. B. The argument is invalid. In symbolic​ form, the argument is    enter your response here. Valid Arguments Direct Reasoning Contrapositive Reasoning Disjunctive Reasoning Transitive Reasoning pright arrowq pright arrowq plogical orq plogical orq pright arrowq p ​~q ​~p ​~q qright arrowr q ​~p q p pright arrowr ​~rright arrow​~p

Invalid Arguments Fallacy of the Converse Fallacy of the Inverse Misuse of Disjunctive Reasoning Misuse of Transitive Reasoning pright arrowq pright arrowq plogical orq plogical orq pright arrowq q ​~p p q qright arrowr p ​~q ​~q ​~p rright arrowp ​~pright arrow​~r

Solution

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Math Problem Analysis

Mathematical Concepts

Propositional Logic
Logical Arguments
Validity Testing

Formulas

Implication (p → q)
Negation (~p)
Contrapositive Reasoning

Theorems

Contrapositive Reasoning
Standard Forms of Logical Validity

Suitable Grade Level

Undergraduate - Logic/Mathematics