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. [tex]\( p \rightarrow q \)[/tex]
[tex]\[ q \][/tex]
[tex]\[ \therefore p \][/tex]

B. [tex]\( p \rightarrow q \)[/tex]
[tex]\[ \sim q \][/tex]
[tex]\[ \therefore \sim p \][/tex]

C. [tex]\( p \rightarrow q \)[/tex]
[tex]\[ \sim p \][/tex]
[tex]\[ \therefore \sim q \][/tex]

D. [tex]\( p \rightarrow q \)[/tex]
[tex]\[ \begin{array}{c} p \\ \therefore q \end{array} \][/tex]



Answer :

To express the given argument symbolically, let's break it down step by step.

1. Identify the statements:
- Statement 1: "If a polygon has exactly three sides, then it is a triangle."
Let's denote this statement as [tex]\( p \rightarrow q \)[/tex], where:
- [tex]\( p \)[/tex]: "A polygon has exactly three sides."
- [tex]\( q \)[/tex]: "It is a triangle."

- Statement 2: "Jeri drew a polygon with exactly three sides."
This matches [tex]\( p \)[/tex], the antecedent of the implication.

- Conclusion: "Therefore, Jeri drew a triangle."
This matches [tex]\( q \)[/tex], the consequent of the implication.

2. Structure of the argument:
- The argument starts with the implication: [tex]\( p \rightarrow q \)[/tex].
- We then assert [tex]\( p \)[/tex].
- From [tex]\( p \rightarrow q \)[/tex] and [tex]\( p \)[/tex], we conclude [tex]\( q \)[/tex].

3. Matching the structure with the provided choices:
- Choice D shows:
[tex]\[ p \rightarrow q \][/tex]
[tex]\[ \begin{array}{c} p \\ \therefore q \end{array} \][/tex]

This matches the given argument exactly.

Hence, the symbolic representation for the argument is:
[tex]\[ \boxed{D} \][/tex]