Question

to attend a particular course, a student must be either at least 13 years old or in grade 9 or higher, but must not yet be 18 years old. let age represent a student’s age and let grade represent the student’s grade level. which of the following expressions evaluates to true if the student is eligible to attend the camp and evaluates to false otherwise?
a
( (age ≥ 13) or (grade ≥ 9) ) and (age ≤ 18)

b
( (age ≥ 13) or (grade ≥ 9) ) and (age < 18)

c
( (age ≥ 13) or (grade ≥ 9) ) or (age ≤ 18)

d
( (age ≥ 13) or (grade ≥ 9) ) or (age < 18)

Explanation:

Step1: Analyze Eligibility Conditions

The student must be either at least 13 years old (age ≥ 13) or in grade 9 or higher (grade ≥ 9), AND must not be less than 18 - wait, no, "must not yet be 18 - years old" means age < 18? Wait, no, "not yet 18" is age < 18? Wait, the problem says "must not yet be 18 - years old", so age < 18? Wait, no, "not yet 18" is age ≤ 17? Wait, no, the options have age ≤ 18 or age < 18. Wait, let's re - read the problem: "a student must be either at least 13 years old or in grade 9 or higher, but must not yet be 18 - years old". So the conditions are: (age ≥ 13 OR grade ≥ 9) AND (age < 18). Wait, no, "not yet 18" is age < 18? Or age ≤ 17? But looking at the options, option A has (age ≥ 13 OR grade ≥ 9) AND (age ≤ 18), option B has (age ≥ 13 OR grade ≥ 9) AND (age < 18), option C has (age ≥ 13 OR grade ≥ 9) OR (age ≤ 18), option D has (age ≥ 13 OR grade ≥ 9) OR (age < 18).

First, the "either...or" is a logical OR, and the "but must not yet be 18" is a logical AND with the OR condition. So the structure should be (Condition1 OR Condition2) AND Condition3, where Condition1: age ≥ 13, Condition2: grade ≥ 9, Condition3: age < 18 (since "not yet 18" means less than 18).

Now let's analyze each option:

• Option A: (age ≥ 13 OR grade ≥ 9) AND (age ≤ 18). But the problem says "not yet 18", which is age < 18, not age ≤ 18. So A is incorrect.
• Option B: (age ≥ 13 OR grade ≥ 9) AND (age < 18). This matches the structure we derived: (Condition1 OR Condition2) AND Condition3, where Condition3 is age < 18.
• Option C: (age ≥ 13 OR grade ≥ 9) OR (age ≤ 18). The OR here is wrong, because we need both the (age ≥13 or grade ≥9) and age < 18 to be true, so it should be AND, not OR. So C is incorrect.
• Option D: (age ≥ 13 OR grade ≥ 9) OR (age < 18). Again, the OR is wrong, we need the AND of the two conditions. So D is incorrect.

Step2: Confirm the Correct Option

By analyzing the logical structure of the eligibility conditions, we see that the correct expression is ( (age ≥ 13) OR (grade ≥ 9) ) AND (age < 18), which is option B.

Answer:

B. $(\text{(age } \geq 13\text{) OR (grade } \geq 9\text{)}) \text{ AND (age } < 18\text{)}$