Final answer:
The Laws of Syllogism and Detachment reveal that if a 14-year-old cannot have a driver's license, they also cannot legally drive a car. These legal discriminations, including age requirements, are examples of how governments ensure public safety within the bounds of the equal protection clause.
Step-by-step explanation:
Understanding the Laws of Syllogism and Detachment
The Laws of Syllogism and Detachment are methods of logical reasoning used to derive conclusions from given statements or premises. In the Law of Detachment, if a conditional statement (if p, then q) is accepted, and p is affirmed to be true, then q must also be concluded to be true. The Law of Syllogism, on the other hand, allows the combination of two conditional statements (if p, then q; if q, then r) to conclude a third conditional statement (if p, then r).
Using these laws, we can evaluate the student's initial premises: "If you don't have your driver's license, then you can't drive a car." (if p, then q), and "If you are 14 years old, then you don't have your driver's license." (if r, then p). The conclusion we can draw through the Law of Syllogism is: "If you are 14 years old, then you can't drive a car." (if r, then q).
This reasoning follows legal discrimination which governments practice by establishing laws for public safety and welfare—such as age restrictions for driving, smoking, and alcohol consumption. It is an example of how the equal protection clause allows for differentiation when public interest is at stake.