Final answer:
The correct answer is option (a): a can be any rational number, b can be any rational number, and c must be a rational number less than b. This is established based on the given inequalities, which indicate the respective relationships among the three rational numbers a, b, and c.
Step-by-step explanation:
The question posed by the student involves understanding and solving inequalities with rational numbers, specifically concerning the relationships between three rational numbers labeled as a, b, and c. In mathematical notation, inequalities are used to show the relative values of numbers, and the symbols > and < indicate 'greater than' and 'less than' respectively.
From the information provided, we have the following inequalities related to a, b, and c:
- a can be any rational number.
- b must be greater than c, which is indicated by b > c.
- c must be a rational number less than b.
This means that the correct answer is: a can be any rational number, b can be any rational number, and c must be a rational number less than b. Therefore, the correct answer to the student's question is option (a).