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

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

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

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

Sagot :

GinnyAnsweridn
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.
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