Geometry

Question Analysis:
This question presents a real-world scenario and requires the student to correctly apply the Law of Detachment to determine a valid conclusion.

Key Concept Explanation:
The Law of Detachment states that if:
p → q (a true conditional statement), and
p is known to be true,
then q must also be true.
The given statement:
p = "A student scores above 90% on the final exam."
q = "They will receive an A in the class."
If p is true, then q must also be true.

Step-by-Step Solution:
Analyze each answer choice:

A) "Jake scored above 90% on the final exam. Therefore, he will receive an A in the class."
p (hypothesis) is true → q (conclusion) must be true ✅
Correct application of the Law of Detachment.

B) "Olivia received an A in the class. Therefore, she must have scored above 90% on the final exam."
Incorrect. This assumes the converse of the statement is true.
Other students might receive an A through extra credit, participation, or other factors.

C) "Liam scored 85% on the final exam. Therefore, he will not receive an A in the class."
Incorrect. The given conditional statement does not say that scoring below 90% guarantees not getting an A.
There could be other ways to earn an A.

D) "Emma studied hard for the final exam. Therefore, she will receive an A in the class."
Incorrect. Studying hard is not part of the given conditional statement.
The hypothesis must match exactly—studying does ...