Question

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

If a line touches a circle only at one point, then it is a tangent.

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

Answer 1

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

If a line touches a circle only at one point, then it is a tangent.

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

Student 4: If a line is not a tangent, then it touches a circle only at one point.

Student 1: If a line does not touch a circle only at one point, then it is a tangent.

Student 3: If a line is not a tangent, then it does not touch a circle only at one point.

Student 2: If a line touches a circle only at one point, then it is not a tangent.

Answer 2

student 3 is correct

Answer 3

thanks

Answer 4

student 3, because If a line is not a tangent, then it does not touch a circle only at one point is correct.

the original is if a, then b.
student b's answer is if -a, then -b.