The contrapositive of the statement "if I am not feeling 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 1: Identify the components of the statement
The original statement can be broken down into two parts:
- Let \( P \): "I am not feeling well."
- Let \( Q \): "I will go to the doctor."

### Step 2: Write the original statement in logical form
The original statement can be expressed in logical terms as:
\[ P \implies Q \]
This means "If \( P \) is true, then \( Q \) is also true."

### Step 3: Formulate the contrapositive
The contrapositive of a statement \( P \implies Q \) is given by:
\[ \neg Q \implies \neg P \]
Where \( \neg \) denotes negation (not). This means we need to negate both \( Q \) and \( P \).

### Step 4: Negate the components
- The negation of \( Q \) ("I will go to the doctor") is "I will not go to the doctor."
- The negation of \( P \) ("I am not feeling well") is "I am feeling well."

### Step 5: Write the contrapositive statement
Putting it all together, the contrapositive statement is:
"If I will not go to the doctor, then I am feeling well."

### Conclusion
Thus, the contrapositive of the statement "If I am not feeling well, then I will go to the doctor" is:
**"If I will not go to the doctor, then I am feeling well."**