Geometry

Question Analysis:
This question directly tests the core principle of the Law of Detachment and whether the student understands its proper application.

Key Concept Explanation:
A conditional statement follows the form:If p, then q(p→q)
The Law of Detachment states that if:
p → q (a true conditional statement), and
p (the hypothesis is true),
then q must also be true.

Step-by-Step Solution:
Let’s consider an example:
Conditional statement: "If a person is a teenager, then they are younger than 20 years old." ✅ (True)
Given information: "Alex is a teenager." ✅ (Hypothesis is true)
Conclusion: "Alex is younger than 20 years old." ✅ (Must be true, according to the Law of Detachment)
Since the conclusion must be true when the hypothesis and conditional statement are true, the given statement in the problem is correct.

Common Mistakes:
Confusing the Law of Detachment with other logical rules (such as the Law of Syllogism).
Thinking the conclusion is only "sometimes" true—when in ...