Question

Given:
p: student achieves 90 percent on the geometry final.
q: student will receive a passing grade in geometry class.
Which statement is logically equivalent to q → p?

If a student achieves 90 percent on the geometry final, then the student will pass geometry class.
If a student passes geometry class, then the student achieved 90 percent on the geometry final.
If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.
If a student did not pass geometry class, then the student did not achieve 90 percent on the geometry final.

Answer 1

q → p is equivalent to its contrapositive ¬p → ¬q. So the logically equivalent statement is:

"If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class."

(Option 3). Note: Option 2 is just a restatement of q → p itself.