Question

Question was provided via image upload.

Explanation:

Identify the given argument structure

Using the Conditional Statements and Hypothesis and Conclusion knowledge points, we first transcribe the original argument components from the image:

• Premise 1: If prices are increased, then consumers will have less disposable income.
• Premise 2: With less disposable income, spending will decrease and the economy will slow down.
• Conclusion: A price increase will slow down the economy.

Let us define the propositions:

• \(p\): Prices are increased.
• \(q\): Consumers have less disposable income.
• \(r\): Spending will decrease and the economy will slow down (or simply, the economy will slow down).

Premise 1 is already in the conditional form: "If \(p\), then \(q\)" (\(p
ightarrow q\)).

Translate Premise 2 to conditional form

Using the Conditional Statements knowledge point, we rewrite Premise 2: "With less disposable income, spending will decrease and the economy will slow down."
The condition (hypothesis) is having less disposable income (\(q\)), and the consequence (conclusion) is that the economy will slow down (\(r\)).
Thus, the conditional form "If \(p\), then \(q\)" for this premise is:
"If consumers have less disposable income, then the economy will slow down."

This matches option B: "If consumers have less disposable income, then the economy will slow down."

Translate the Conclusion to conditional form

Using the Conditional Statements knowledge point, we rewrite the Conclusion: "A price increase will slow down the economy."
The condition is a price increase (\(p\)), and the consequence is that the economy will slow down (\(r\)).
Thus, the conditional form is:
"If prices are increased, then the economy will slow down."

This matches option A: "If prices are increased, then the economy will slow down."

Determine the validity of the argument

Using the Hypothetical Syllogism and Logical Validity knowledge points:

• Premise 1: \(p

ightarrow q\)

• Premise 2: \(q

ightarrow r\)

• Conclusion: \(p

ightarrow r\)

This forms a transitive chain:

$$ p ightarrow q \quad \text{and} \quad q ightarrow r \implies p ightarrow r $$

Since there is a clear, unbroken chain of conditional implications from "prices are increased" to "the economy will slow down," the argument is logically valid.

This matches option B: "Yes, because there is a clear chain from 'prices are increased' to 'the economy will slow down.'"

Answer:

Question 1

• (A) If prices are increased, then consumers will have less disposable income.
• (B) If consumers have less disposable income, then the economy will slow down. (Correct answer)
• (C) If prices are increased, then the economy will slow down.
• (D) With less disposable income, spending will decrease and the economy will slow down.

Question 2

• (A) If prices are increased, then the economy will slow down. (Correct answer)
• (B) A price increase will slow down the economy.
• (C) If consumers have less disposable income, then the economy will slow down.
• (D) If prices are increased, then consumers will have less disposable income.

Question 3

• (A) Yes, because both of the premises are true.
• (B) Yes, because there is a clear chain from "prices are increased" to "the economy will slow down." (Correct answer)
• (C) No, because there is no clear chain from "prices are increased" to "the economy will slow down."