The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is:

To solve this problem, we need to find the contrapositive of the given statement: "if I am not feeling well, then I will go to the doctor."

First, recall that for any conditional statement of the form "If P, then Q," the contrapositive is "If not Q, then not P." The contrapositive is logically equivalent to the original statement.

Identify the components of the given statement:

• P: "I am not feeling well"
• Q: "I will go to the doctor"

So the statement is: If P, then Q.

Now, form the contrapositive: If not Q, then not P.

Determine not Q and not P:

• not Q: Negation of "I will go to the doctor" is "I will not go to the doctor."
• not P: Negation of "I am not feeling well" is "I am feeling well" (since two negatives cancel out).

Therefore, the contrapositive is: "If I will not go to the doctor, then I am feeling well."

Now, compare this with the options:

• Option A: "if I will go to the doctor, then I am not feeling well" → This is "If Q, then P," which is the converse, not the contrapositive.
• Option B: "if I am feeling well, then I will not go to the doctor" → This is "If not P, then not Q," which is the inverse, not the contrapositive.
• Option C: "if I will not go to the doctor, then I am feeling well" → This matches our contrapositive exactly: "If not Q, then not P."
• Option D: "if I will go to the doctor, then I am feeling well" → This is "If Q, then not P," which is neither the contrapositive nor logically equivalent.

Hence, the correct answer is Option C.