Final answer:
Using the Law of Detachment, we can infer that since "You will go to the movies with your friend" is true, then the statement "Your parents let you borrow the car" is also true. The contrary statement cannot be concluded with this law.
Step-by-step explanation:
Law of Detachment in Logical Reasoning
The Law of Detachment, also known as modus ponens, is a principle used in deductive reasoning in mathematics. This law states that if a conditional statement ("if p, then q") is accepted as true, and the antecedent (p) is also true, then the consequent (q) must also be true. In the scenario provided:
- If your parents let you borrow the car, then you will go to the movies with your friend.
- You will go to the movies with your friend.
Using the Law of Detachment, we can conclude that "Your parents let you borrow the car" must be true since the condition immutably leads to the outcome, and the outcome is confirmed to be true.
However, the statement "Your parents didn't let you borrow the car." cannot be concluded from the information given using the Law of Detachment because this would require the Law of Contrapositive, which is different from the Law of Detachment.
Use your prior knowledge of the situation and logical reasoning to understand the outcome, but avoid letting personal opinions cloud your judgment. It helps to stay within the facts and known information to draw accurate conclusions.