Geometry

Question Analysis:
This question examines a common logical misconception—whether the truth of the conclusion guarantees the truth of the hypothesis.

Key Concept Explanation:
A conditional statement is written as: If p, then q(p→q)
The Law of Detachment states that if p → q is true and p is true, then q must also be true.
However, the reverse is not always true.
Just because q is true, it does not necessarily mean that p is true.

Step-by-Step Solution:
Consider an example:
Conditional statement: "If it is raining, then the ground is wet." ✅ (True statement)
Conclusion: "The ground is wet." ✅ (True)
Can we conclude that "It is raining"? ❌ No—the ground might be wet due to other reasons (e.g., someone watering the plants).
Since the hypothesis does not necessarily follow from the truth of the conclusion, the statement is false.

Common Mistakes:
Confusing the Law of Detachment with the Converse Error (i.e., assuming "If q, then p").