Question

if necessary, write the given argument as a chain of conditional propositions that have the form if p, then q. then determine the validity of the entire argument.

premise: if prices are increased, then consumers will have less disposable income.
premise: with less disposable income, spending will decrease and the economy will slow down.
conclusion: a price increase will slow down the economy.

write the second premise as a conditional proposition that has the form if p, then q. choose the correct answer below.

a. if prices are increased, then consumers will have less disposable income.
b. if prices are increased, then the economy will slow down.
c. if consumers have less disposable income, then the economy will slow down.
d. with less disposable income, spending will decrease and the economy will slow down.

Explanation:

Identify the target premise

The question asks to write the second premise as a conditional proposition in the form "if \(p\), then \(q\)".
The second premise in the argument is:
"With less disposable income, spending will decrease and the economy will slow down."

Translate to conditional form

Using the Conditional Statements knowledge point:

• The condition (hypothesis \(p\)) is having less disposable income.
• The consequence (conclusion \(q\)) is that the economy will slow down (which encompasses the spending decrease and economic slowdown).
• Thus, the conditional statement is: "If consumers have less disposable income, then the economy will slow down."

Match with options

• Option A represents the first premise.
• Option B represents the conclusion of the entire argument.
• Option C represents the second premise rewritten in "if \(p\), then \(q\)" form.
• Option D is simply the original second premise without rewriting.

Answer:

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