Question
To be eligible for a particular ride at an amusement park, a person must be at least 12 years old and must be between 50 and 80 inches tall, inclusive.
Let age represent a person’s age, in years, and let height represent the person’s height, in inches.
Question
2
Mark for Review
Which of the following expressions evaluates to true if and only if the person is eligible for the ride?
(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))
Option A,(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))
(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))
Option B,(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))
(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))
Option C,(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))
(age ≥ 12) OR ((height ≥ 50) AND (height ≤ 80))
Let age represent a person’s age, in years, and let height represent the person’s height, in inches.
Question
2
Mark for Review
Which of the following expressions evaluates to true if and only if the person is eligible for the ride?
(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))
Option A,(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))
(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))
Option B,(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))
(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))
Option C,(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))
(age ≥ 12) OR ((height ≥ 50) AND (height ≤ 80))
Answers
GPT-4o mini
To determine which expression evaluates to true if and only if the person is eligible for the ride, let's break down the eligibility criteria:
1. **Age**: The person must be at least 12 years old. This means:
- \( \text{age} \geq 12 \)
2. **Height**: The person must be between 50 and 80 inches tall, inclusive. This means:
- \( \text{height} \geq 50 \) AND \( \text{height} \leq 80 \)
The complete eligibility condition can be expressed logically as:
- \( (\text{age} \geq 12) \) AND \( ((\text{height} \geq 50) \) AND \( (\text{height} \leq 80)) \)
Now let's evaluate the options:
- **Option A**:
\((\text{age} \geq 12) \) AND \((\text{height} \geq 50) \) AND \((\text{height} \leq 80)\)
This option matches the eligibility condition.
- **Option B**:
\((\text{age} \geq 12) \) AND \((\text{height} \leq 50) \) AND \((\text{height} \geq 80)\)
This option is incorrect because it states that height must be both less than or equal to 50 and greater than or equal to 80, which is impossible.
- **Option C**:
\((\text{age} \geq 12) \) AND \((\text{height} \leq 50) \) OR \((\text{height} \geq 80)\)
This option is incorrect because it allows for the person to be below 50 inches or above 80 inches (not the specified range).
- **Option D**:
\((\text{age} \geq 12) \) OR \((\text{height} \geq 50) \) AND \((\text{height} \leq 80)\)
This option is also incorrect because it allows for being eligible if the person meets only one of the criteria instead of both.
Based on the above evaluation, **Option A** is the only expression that accurately evaluates to true if and only if the person is eligible for the ride.
1. **Age**: The person must be at least 12 years old. This means:
- \( \text{age} \geq 12 \)
2. **Height**: The person must be between 50 and 80 inches tall, inclusive. This means:
- \( \text{height} \geq 50 \) AND \( \text{height} \leq 80 \)
The complete eligibility condition can be expressed logically as:
- \( (\text{age} \geq 12) \) AND \( ((\text{height} \geq 50) \) AND \( (\text{height} \leq 80)) \)
Now let's evaluate the options:
- **Option A**:
\((\text{age} \geq 12) \) AND \((\text{height} \geq 50) \) AND \((\text{height} \leq 80)\)
This option matches the eligibility condition.
- **Option B**:
\((\text{age} \geq 12) \) AND \((\text{height} \leq 50) \) AND \((\text{height} \geq 80)\)
This option is incorrect because it states that height must be both less than or equal to 50 and greater than or equal to 80, which is impossible.
- **Option C**:
\((\text{age} \geq 12) \) AND \((\text{height} \leq 50) \) OR \((\text{height} \geq 80)\)
This option is incorrect because it allows for the person to be below 50 inches or above 80 inches (not the specified range).
- **Option D**:
\((\text{age} \geq 12) \) OR \((\text{height} \geq 50) \) AND \((\text{height} \leq 80)\)
This option is also incorrect because it allows for being eligible if the person meets only one of the criteria instead of both.
Based on the above evaluation, **Option A** is the only expression that accurately evaluates to true if and only if the person is eligible for the ride.