Question
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 eligibility for the ride, a person must meet two conditions:
1. The person's age must be at least 12 years old.
2. The person's height must be between 50 and 80 inches, inclusive.
This can be expressed logically using the following expression:
- **Age Condition:** `age ≥ 12`
- **Height Condition:** `height ≥ 50 AND height ≤ 80`
Combining these conditions, the correct expression to evaluate whether a person is eligible for the ride is:
`(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))`
Now let's evaluate the provided options:
- **Option A:** `(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))` - This is TRUE if the person meets both the age and height conditions. **[Correct]**
- **Option B:** `(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))` - This is FALSE because height cannot be less than or equal to 50 AND greater than or equal to 80 at the same time.
- **Option C:** `(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))` - This is FALSE as it does not ensure that height is within the required range of 50 to 80 inches.
- **Option D:** `(age ≥ 12) OR ((height ≥ 50) AND (height ≤ 80))` - This is FALSE as eligibility requires both conditions to be met, not just one.
Therefore, the correct expression that evaluates to true if and only if the person is eligible for the ride is **Option A**: *(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))*.
1. The person's age must be at least 12 years old.
2. The person's height must be between 50 and 80 inches, inclusive.
This can be expressed logically using the following expression:
- **Age Condition:** `age ≥ 12`
- **Height Condition:** `height ≥ 50 AND height ≤ 80`
Combining these conditions, the correct expression to evaluate whether a person is eligible for the ride is:
`(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))`
Now let's evaluate the provided options:
- **Option A:** `(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))` - This is TRUE if the person meets both the age and height conditions. **[Correct]**
- **Option B:** `(age ≥ 12) AND ((height ≤ 50) AND (height ≥ 80))` - This is FALSE because height cannot be less than or equal to 50 AND greater than or equal to 80 at the same time.
- **Option C:** `(age ≥ 12) AND ((height ≤ 50) OR (height ≥ 80))` - This is FALSE as it does not ensure that height is within the required range of 50 to 80 inches.
- **Option D:** `(age ≥ 12) OR ((height ≥ 50) AND (height ≤ 80))` - This is FALSE as eligibility requires both conditions to be met, not just one.
Therefore, the correct expression that evaluates to true if and only if the person is eligible for the ride is **Option A**: *(age ≥ 12) AND ((height ≥ 50) AND (height ≤ 80))*.