The contrapositive of the statement "I go to school if it does not rain" is

Options

A. If it rains, I do not go to school
B. If I do not go to school, it rains
C. If it rains, I go to school
D. If I go to school, it rains

Answer

To find the contrapositive of the statement "I go to school if it does not rain," we can follow these steps:

### Step 1: Identify the components of the statement
The statement can be broken down into two parts:
- Let \( P \) represent "It does not rain."
- Let \( Q \) represent "I go to school."

### Step 2: Write the implication
The original statement can be expressed as an implication:
- If \( P \) (It does not rain), then \( Q \) (I go to school).
- This can be written as \( P \implies Q \).

### Step 3: Find the contrapositive
The contrapositive of an implication \( P \implies Q \) is given by \( \neg Q \implies \neg P \), where \( \neg \) denotes negation.
- Here, \( \neg Q \) means "I do not go to school."
- \( \neg P \) means "It rains."

So, the contrapositive statement becomes:
- If I do not go to school, then it rains.
- This can be written as \( \neg Q \implies \neg P \).

### Step 4: Write the final contrapositive statement
Thus, the contrapositive of the original statement "I go to school if it does not rain" is:
- "If I do not go to school, then it rains."

### Conclusion
The correct answer is: **If I do not go to school, it rains.**

---