To solve the question, we need to translate the given argument into its symbolic representation logically.
Here is the argument provided:
1. If a polygon has exactly three sides (p), then it is a triangle (q).
2. Jeri drew a polygon with exactly three sides (p).
3. Therefore, Jeri drew a triangle (q).
Let's analyze this step-by-step using symbolic logic:
1. The first statement, "If a polygon has exactly three sides, then it is a triangle," can be represented as [tex]\( p \rightarrow q \)[/tex].
2. The second statement, "Jeri drew a polygon with exactly three sides," is given as [tex]\( p \)[/tex].
3. The conclusion drawn from these statements is "Therefore, Jeri drew a triangle," signified as [tex]\( \therefore q \)[/tex].
From the above analysis, we see that the given statements form an argument where:
- The first line [tex]\( p \rightarrow q \)[/tex] represents the conditional statement.
- The second line [tex]\( p \)[/tex] represents the given fact.
- The conclusion line [tex]\( \therefore q \)[/tex] is derived from the premises given.
So, the symbolic representation resembling this argument must reflect this logical sequence.
The correct choice is:
D.
[tex]\[
\begin{tabular}{|c|}
\hline
p \rightarrow q \\
\hline
p \\
\hline
\therefore q \\
\hline
\end{tabular}
\][/tex]
This is the symbolic representation of the logical argument provided in the question.
