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Chapter 3: Problem 78

Write an original argument in words for the contrapositive reasoning form.

Short Answer

Expert verified
Contrapositive argument: If the alarm did not ring in the morning and woke nobody up, this implies that the alarm wasn't set the night before because if it was, it would have rung and awakened everyone.

Step by step solution

01

- Understanding Contrapositive Reasoning

It's crucial to understand how contrapositive reasoning works. The core structure of contrapositive reasoning lies in the formula: If P, then Q. Contrapositive of this statement would be: If not Q, then not P.
02

- Constructing P and Q

Now, let's choose a hypothetical situation to construct P and Q. Let P be 'The alarm is set', and Q be 'The alarm rings in the morning'. So, our initial statement now becomes, If the alarm is set, then the alarm rings in the morning.
03

- Statement Contrapositive

We have the statement, now let's form the contrapositive. According to its definition, the contrapositive will be, If the alarm did not ring in the morning, then the alarm was not set.
04

- Argument

Now let's form the argument, If the alarm did not ring in the morning and woke nobody up, this implies that the alarm wasn't set the night before because if it was, it would have rung and awakened everyone.

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Most popular questions from this chapter

Use Euler diagrams to determine whether each argument is valid or invalid. All insects have six legs. No spiders have six legs. Therefore, no spiders are insects.

Use Euler diagrams to determine whether each argument is valid or invalid. All multiples of 6 are multiples of 3 . Eight is not a multiple of \(6 .\) Therefore, 8 is not a multiple of 3 .

No animals that eat meat are vegetarians. No cat is a vegetarian. Felix is a cat. Therefore,,\(.\) a. Felix is a vegetarian. b. Felix is not a vegetarian. c. Felix eats meat. d. All animals that do not eat meat are vegetarians.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &q \rightarrow \sim p \\ &q \wedge r \\ &\therefore r \rightarrow p \end{aligned} $$

Determine whether each argument is valid or invalid. No \(A\) are \(B\), no \(B\) are \(C\), and no \(C\) are \(D\). Thus, no \(A\) are \(D\).
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