Question

what is the symbolic representation for this argument? if a polygon has exactly three sides, then it is a triangle. jeri drew a polygon with exactly three sides. therefore, jeri drew a triangle. a. \\( p \
ightarrow q \\) \\( q \\) \\( \therefore p \\) b. \\( p \
ightarrow q \\) \\( \sim q \\) \\( \therefore \sim p \\) c. \\( p \
ightarrow q \\) \\( \sim p \\) \\( \therefore \sim q \\) d. \\( p \
ightarrow q \\) \\( p \\) \\( \therefore q \\)

Explanation:

Step1: Define Propositions

Let \( p \) be "a polygon has exactly three sides" and \( q \) be "it is a triangle".

Step2: Analyze the Argument Structure

• The first statement is a conditional: \( p

ightarrow q \) (If \( p \), then \( q \)).

• The second statement is \( p \) (Jeri drew a polygon with exactly three sides, so \( p \) is true).
• The conclusion is \( q \) (Therefore, Jeri drew a triangle, so \( q \) follows).
• This matches the structure \( p

ightarrow q \), \( p \), \( \therefore q \), which is option D.

Answer:

D. \( \boldsymbol{p
ightarrow q} \)
\( \boldsymbol{p} \)
\( \boldsymbol{\therefore q} \)