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))
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))
Answers
GPT-4o mini
To determine which expression evaluates to true if and only if a person is eligible for the ride, we need to analyze the conditions provided:
1. A person must be at least 12 years old: \( age \geq 12 \)
2. A person must be between 50 and 80 inches tall, inclusive: \( height \geq 50 \) AND \( height \leq 80 \)
Now, let's evaluate the options one by one:
- **Option A**: \((age \geq 12) AND ((height \geq 50) AND (height \leq 80))\)
This expression states that both conditions for eligibility must be true:
- The age must be at least 12.
- The height must be between 50 and 80 inches (inclusive).
This matches exactly with the requirements.
- **Option B**: \((age \geq 12) AND ((height \leq 50) AND (height \geq 80))\)
This expression states that a person must be at least 12 years old, but it incorrectly requires that the height must be less than or equal to 50 inches AND greater than or equal to 80 inches at the same time, which is impossible. Thus, this option cannot be true.
- **Option C**: \((age \geq 12) AND ((height \leq 50) OR (height \geq 80))\)
This expression states that a person must be at least 12 years old and must be either less than or equal to 50 inches OR greater than or equal to 80 inches. This is not a valid representation of the height requirement, as it allows heights that are outside the range of eligibility.
Therefore, the only option that evaluates to true if and only if the person is eligible for the ride is:
**Option A**: \((age \geq 12) AND ((height \geq 50) AND (height \leq 80))\)
1. A person must be at least 12 years old: \( age \geq 12 \)
2. A person must be between 50 and 80 inches tall, inclusive: \( height \geq 50 \) AND \( height \leq 80 \)
Now, let's evaluate the options one by one:
- **Option A**: \((age \geq 12) AND ((height \geq 50) AND (height \leq 80))\)
This expression states that both conditions for eligibility must be true:
- The age must be at least 12.
- The height must be between 50 and 80 inches (inclusive).
This matches exactly with the requirements.
- **Option B**: \((age \geq 12) AND ((height \leq 50) AND (height \geq 80))\)
This expression states that a person must be at least 12 years old, but it incorrectly requires that the height must be less than or equal to 50 inches AND greater than or equal to 80 inches at the same time, which is impossible. Thus, this option cannot be true.
- **Option C**: \((age \geq 12) AND ((height \leq 50) OR (height \geq 80))\)
This expression states that a person must be at least 12 years old and must be either less than or equal to 50 inches OR greater than or equal to 80 inches. This is not a valid representation of the height requirement, as it allows heights that are outside the range of eligibility.
Therefore, the only option that evaluates to true if and only if the person is eligible for the ride is:
**Option A**: \((age \geq 12) AND ((height \geq 50) AND (height \leq 80))\)