To determine the symbolic representation for the given argument, let's first define the statement variables:
- Let [tex]\( p \)[/tex] be the statement "A polygon has exactly three sides."
- Let [tex]\( q \)[/tex] be the statement "It is a triangle."
The argument given is:
1. If a polygon has exactly three sides, then it is a triangle. ([tex]\( p \rightarrow q \)[/tex])
2. Jeri drew a polygon with exactly three sides. ([tex]\( p \)[/tex])
From these statements, we can conclude:
3. Therefore, Jeri drew a triangle. ([tex]\( q \)[/tex])
By examining the structure, we see that the form of the argument can be written symbolically as:
1. [tex]\( p \rightarrow q \)[/tex]
2. [tex]\( p \)[/tex]
3. [tex]\( \therefore q \)[/tex]
This corresponds to option D:
D.
[tex]\[
\begin{array}{l}
p \rightarrow q \\
p \\
\therefore q
\end{array}
\][/tex]
Thus, the argument follows the logical form known as modus ponens. This form validates that if [tex]\( p \rightarrow q \)[/tex] and [tex]\( p \)[/tex] are both true, then [tex]\( q \)[/tex] must also be true.
