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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]\[
\begin{tabular}{|c|}
\hline
\rho \rightarrow q \\
\hline
q \\
\hline
\therefore p \\
\hline
\end{tabular}
\][/tex]

B.
[tex]\[
\begin{tabular}{|c|}
\hline
p \rightarrow q \\
\hline
\neg q \\
\hline
\therefore \neg p \\
\hline
\end{tabular}
\][/tex]

C.
[tex]\[
\begin{tabular}{|c|}
\hline
p \rightarrow q \\
\hline
\neg p \\
\hline
\therefore \neg q \\
\hline
\end{tabular}
\][/tex]

D.
[tex]\[
\begin{tabular}{|c|}
\hline
p \rightarrow q \\
\hline
p \\
\hline
\therefore q \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
Let's break down the argument and see which option correctly represents it using symbolic logic.

1. Statement 1: "If a polygon has exactly three sides, then it is a triangle."

This statement can be written in symbolic form as:
[tex]\( p \rightarrow q \)[/tex]

where:
[tex]\( p \)[/tex]: "A polygon has exactly three sides."
[tex]\( q \)[/tex]: "It is a triangle."

2. Statement 2: "Jeri drew a polygon with exactly three sides."

This statement can be represented as:
[tex]\( p \)[/tex]

3. Conclusion: "Therefore, Jeri drew a triangle."

Based on the given statements, this conclusion can be written as:
[tex]\( \therefore q \)[/tex]

Putting these together, we get the structure:
- [tex]\( p \rightarrow q \)[/tex]
- [tex]\( p \)[/tex]
- [tex]\( \therefore q \)[/tex]

This format corresponds to the option:
[tex]\[ \begin{tabular}{|c|} \hline $p \rightarrow q$ \\ \hline $p$ \\ \hline $\therefore q$ \\ \hline \end{tabular} \][/tex]

Therefore, the correct symbolic representation for this argument is option D.
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