In a geometry class, the students were asked to write statements that are logically equivalent to the statement shown below.

If a line intersects a circle at exactly two points, then it is a secant.

Below are the responses of four students. Which student’s response is correct?

Question

In a geometry class, the students were asked to write statements that are logically equivalent to the statement shown below. 
  
If a line intersects a circle at exactly two points, then it is a secant. 
  
Below are the responses of four students. Which student’s response is correct?

anonymous · Answer

Student 4: If a line is not a secant, then it does not intersect the circle at exactly two points. 

 Student 3: If a line is not a secant, then it intersects the circle at exactly two points.

 Student 1: If a line intersects a circle at exactly two points, then it is not a secant.

 Student 2: If a line does not intersect a circle at exactly two points, then it is a secant.

anonymous · Answer

I forget what it's called but the given statement is "P implies Q"
P = a line intersects a circle at exactly two points
Q = it is a secant
If P is correct, then Q must be correct.

The logically equivalent statement is "not P implies not Q".  Can you see which statement of the 4 corresponds to that?

anonymous · Answer

I think it is student 4 that is correct

anonymous · Answer

oops I messed up.  Not Q implies not P.

anonymous · Answer

And yes, you're correct.  Student 4's answer is logically equivalent to what's given.

anonymous · Answer

Yes! Thank you so much! I gave you a medal! :)

anonymous · Answer

Makes my day.