The contra-positive of the statement "if I am not feel- ing well, then I will go to the doctor" is ·

Options

A. If I am feeling well, then I will not go to the doctor
B. If I will go to the doctor, then I am feeling well
C. If I will not go to the doctor, then I am feeling well
D. If I will go to the doctor, then I am not feeling well

Answer

To find the contrapositive of the statement "If I am not feeling well, then I will go to the doctor," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Statements**:
- Let \( P \) be the statement "I am not feeling well."
- Let \( Q \) be the statement "I will go to the doctor."

2. **Write the Original Statement**:
- The original statement can be expressed in logical form as \( P \implies Q \) (If \( P \), then \( Q \)).

3. **Find the Negations**:
- The negation of \( P \) (not feeling well) is \( \neg P \): "I am feeling well."
- The negation of \( Q \) (going to the doctor) is \( \neg Q \): "I will not go to the doctor."

4. **Formulate the Contrapositive**:
- The contrapositive of the statement \( P \implies Q \) is \( \neg Q \implies \neg P \).
- This translates to: "If I will not go to the doctor, then I am feeling well."

5. **Final Statement**:
- Therefore, the contrapositive of the original statement is: "If I will not go to the doctor, then I am feeling well."