In Exercises 17-20, use the Law of Detachment to determine...

In Exercises $17-20,$ use the Law of Detachment to determine what you can conclude from the given information, if possible.
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.

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Key Concepts

Law of Detachment

The Law of Detachment, also known as modus ponens, is a fundamental rule in logic. It states that if a conditional statement is accepted as true, and the antecedent (the 'if' part) is true, then the consequent (the 'then' part) must also be true. This rule allows one to conclude the truth of the consequent when provided with a true antecedent in a valid conditional statement.

Conditional Statement

A conditional statement is a logical expression typically formatted as 'If p, then q', where p is the antecedent and q is the consequent. This construct is essential in both everyday reasoning and formal logical arguments because it establishes a cause-effect relationship that can be used to deduce further inferences in a logical framework.

Affirming the Consequent

Affirming the consequent is a logical fallacy that occurs when one assumes that if 'if p, then q' is true and q is true, then p must be true. This form of reasoning is invalid since there could be other reasons for q being true aside from p. Hence, knowing that q is true does not allow us to definitively conclude that the antecedent p is true.

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