Answer :
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.
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.
