Question

The argument form called modus tollens looks like this: $$ \begin{aligned} & p \supset q \\ & \therefore \sim q \end{aligned} $$ Use truth tables to show that this argument form is valid.

   The argument form called modus tollens looks like this:
$$
\begin{aligned}
& p \supset q \\
& \therefore \sim q
\end{aligned}
$$

Use truth tables to show that this argument form is valid.
Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic
Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic
Walter… 9th Edition
Chapter 6, Problem 20 ↓

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In modus tollens, we have two statements: \( p \supset q \) (if \( p \) then \( q \)) and \( \sim q \) (not \( q \)). We want to show that if both of these statements are true, then \( \sim p \) (not \( p \)) must also be true.  Show more…

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The argument form called modus tollens looks like this: $$ \begin{aligned} & p \supset q \\ & \therefore \sim q \end{aligned} $$ Use truth tables to show that this argument form is valid.
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Key Concepts

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Modus Tollens
Modus tollens is a fundamental rule of inference in propositional logic. It states that if an implication 'if p then q' is true and the consequent q is false, then the antecedent p must also be false. This logical pattern is used to deduce the falsity of the proposition p on the basis that its truth would lead to the truth of q, which contradicts the observation that q is false.
Truth Tables
Truth tables are a systematic tool used in logic to list all possible truth values of propositions and their combinations. They help in evaluating the validity of logical expressions by showing how the truth of premises corresponds to the truth of the conclusion, covering all possible scenarios.
Logical Validity
Logical validity is the concept that an argument is valid if, in every possible case where all the premises are true, the conclusion is also true. It means that the truth of the premises guarantees the truth of the conclusion, ensuring there is no counterexample where the premises hold but the conclusion fails.
Conditional Statements
Conditional statements are logical expressions typically formulated in the 'if p then q' format. They are central to propositional logic, as they establish a relationship between an antecedent (p) and a consequent (q), serving as the basis for many inference techniques including modus tollens.

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Use truth tables to show that the argument forms referred to in 13-21 are valid. Indicate which columns represent the premises and which represent the conclusion, and include a sentence explaining how the truth table supports your answer. Your explanation should show that you understand what it means for a form of argument to be valid. 13. Modus Tollens c: p V q p: p V q ~r: p V q - r

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