Geometry

Question Analysis:
This question involves identifying which option represents an incorrect use of the Law of Detachment.
The main focus is on understanding the logical structure of conditional statements and recognizing when the Law of Detachment is misapplied.

Key Concept Explanation:
The Law of Detachment states that if a conditional statement ("If P, then Q") is true, and P is true, then Q must also be true.
However, it does not allow us to reverse the conditional statement ("If Q, then P") without additional information.

Step-by-Step Solution:
Option A:
Statement: If a shape is a rectangle, then it has four right angles. Shape R is a rectangle, so it has four right angles.
Analysis: The Law of Detachment is correctly applied. P is true (Shape R is a rectangle), so Q must also be true (it has four right angles).
Conclusion: This is valid.

Option B:
Statement: If a student attends all classes, then they will pass the course. Emma attended all classes, so she passed the course.
Analysis: The Law of Detachment is correctly applied. P is true (Emma attended all classes), so Q must also be true (she passed the course).
Conclusion: This is valid.

Option C:
Statement: If a number is even, then it is divisible by 2. The number 14 is even, so it is divisibl...