Question

for a particular ride at an amusement park, a person must be at least 12 years old and must be 50 and 80 inches tall, inclusive. represent the persons height, in inches. 13 mark for review which of the following expressions evaluates to true if and only if the person is eligible for the ride? a {age ≥ 12} and {height ≥ 50} and {height ≤ 80} b {age ≥ 12} and {height ≤ 50} and {height ≥ 80} c {age ≥ 12} and {(height ≤ 50) or (height ≥ 80)} d {age ≥ 12} or {(height ≥ 50) and (height ≤ 80)}

Explanation:

The problem is about determining the correct logical expression for a person to be eligible for a ride: age at least 12 and height between 50 and 80 inches (inclusive? Or exclusive? The left text says "50 and 80 inches tall, exclusive" maybe? Wait, the options: Let's parse. The eligibility is age ≥12 AND (height ≥50 AND height ≤80) (assuming between 50 and 80, including or excluding? But looking at options, option B is (age ≥12) AND (height ≥50) AND (height ≤80). Wait, the left text: "must be at least 12 years old and must be 50 and 80 inches tall, exclusive" – maybe 50 < height <80? But the options: Let's check each. Option A: (age ≥12) AND (height ≥50) AND (height ≤80) – but maybe the original condition is age ≥12 and height between 50 and 80 (inclusive or exclusive). Wait, the question is "Which of the following expressions evaluates to True if and only if the person is eligible for the ride". So eligibility: age ≥12, and height ≥50, and height ≤80 (assuming between 50 and 80, inclusive). So the logical AND between age ≥12, height ≥50, and height ≤80. So option B: (age ≥12) AND (height ≥50) AND (height ≤80) – that's the correct combination. Option A has a typo? Wait, option B's text: "(age ≥ 12) AND (height ≥ 50) AND (height ≤ 80)". Yes, that's the correct logical conjunction: all three conditions (age, min height, max height) must be true. So the correct option is B.

Answer:

B. (age ≥ 12) AND (height ≥ 50) AND (height ≤ 80)