Geometry

Question Analysis:
This question directly tests the fundamental definition of the Law of Detachment in logic.
Understanding this concept is crucial for applying it correctly in geometry problems.

Key Concept Explanation:
A conditional statement is written in the form: If p, then q
where p is the hypothesis and q is the conclusion.
The Law of Detachment states:
If p → q is true, and p is also true, then q must be true.

Step-by-Step Solution:
Examine each option carefully:
A: This describes the converse fallacy (invalid reasoning).
Just because the conclusion is true does not mean the hypothesis must be true.
B: This correctly defines the Law of Detachment.
C: This incorrectly assumes that a conditional statement and its converse are always both true.
This is not necessarily the case.
D: A false conditional statement does not mean both parts are false.
A conditional statement is false only when the hypothesis is true, but the conclusion is false.
The correct answer is B.

Option Analysis:
A: Incorrect. It reverses logical reasoning.
B: Correct. It follows the definition of the Law of Detachment.
C: Incorrect. The converse of a conditional statement is no...