Question

consider the following simple statements.

\\(t\\): the radial tires are included.
\\(s\\): the sunroof is extra.
\\(w\\): wi-fi is optional.

translate the following symbolic compound statement into words:

\\\sim s \wedge \sim w\\

• the sunroof is extra and wi-fi is optional.
• the sunroof is not extra and wi-fi is not optional.
• the sunroof is not extra, or wi-fi is not optional.
• the sunroof is extra or wi-fi is optional.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"direct_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Logical Operators",
"Logical Statement"
],
"new_concepts": [],
"current_concepts": [
"Logical Operators",
"Logical Statement"
]
}
</pre_analysis>

<reasoning>

Identify the components of the symbolic statement

\[

$$\begin{aligned} &s: \text{The sunroof is extra.} \\ &w: \text{Wi-Fi is optional.} \\ &\sim s: \text{The sunroof is not extra.} \\ &\sim w: \text{Wi-Fi is not optional.} \end{aligned}$$

\]

Translate the logical connective

\[

$$\begin{aligned} &\wedge: \text{and} \end{aligned}$$

\]

Combine the translated components

\[

$$\begin{aligned} &\sim s \wedge \sim w: \text{The sunroof is not extra and Wi-Fi is not optional.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The sunroof is extra and Wi-Fi is optional.</mcq-option>
<mcq-correct>The sunroof is not extra and Wi-Fi is not optional.</mcq-correct>
<mcq-option>The sunroof is not extra, or Wi-Fi is not optional.</mcq-option>
<mcq-option>The sunroof is extra or Wi-Fi is optional.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Logical Statement"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"direct_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Logical Operators",
"Logical Statement"
],
"new_concepts": [],
"current_concepts": [
"Logical Operators",
"Logical Statement"
]
}
</pre_analysis>

<reasoning>

Identify the components of the symbolic statement

\[

$$\begin{aligned} &s: \text{The sunroof is extra.} \\ &w: \text{Wi-Fi is optional.} \\ &\sim s: \text{The sunroof is not extra.} \\ &\sim w: \text{Wi-Fi is not optional.} \end{aligned}$$

\]

Translate the logical connective

\[

$$\begin{aligned} &\wedge: \text{and} \end{aligned}$$

\]

Combine the translated components

\[

$$\begin{aligned} &\sim s \wedge \sim w: \text{The sunroof is not extra and Wi-Fi is not optional.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The sunroof is extra and Wi-Fi is optional.</mcq-option>
<mcq-correct>The sunroof is not extra and Wi-Fi is not optional.</mcq-correct>
<mcq-option>The sunroof is not extra, or Wi-Fi is not optional.</mcq-option>
<mcq-option>The sunroof is extra or Wi-Fi is optional.</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Logical Statement"
]
}
</post_analysis>