Answer the following questions
Write the converse, inverse and contrapositive of the statement "If it snows, then they do not drive the car"

Answer

To solve the problem, we need to identify the original statement and then derive its converse, inverse, and contrapositive.

### Step 1: Identify the Original Statement
The original statement is: "If it snows, then they do not drive the car."
- Let \( P \): "It snows."
- Let \( Q \): "They do not drive the car."

This can be expressed in logical form as:
\[ P \implies Q \]

### Step 2: Write the Converse
The converse of a statement \( P \implies Q \) is \( Q \implies P \).
- Converse: "If they do not drive the car, then it snows."

### Step 3: Write the Inverse
The inverse of a statement \( P \implies Q \) is \( \neg P \implies \neg Q \).
- Inverse: "If it does not snow, then they drive the car."

### Step 4: Write the Contrapositive
The contrapositive of a statement \( P \implies Q \) is \( \neg Q \implies \neg P \).
- Contrapositive: "If they drive the car, then it does not snow."

### Summary of Results
1. **Original Statement**: If it snows, then they do not drive the car. ( \( P \implies Q \) )
2. **Converse**: If they do not drive the car, then it snows. ( \( Q \implies P \) )
3. **Inverse**: If it does not snow, then they drive the car. ( \( \neg P \implies \neg Q \) )
4. **Contrapositive**: If they drive the car, then it does not snow. ( \( \neg Q \implies \neg P \) )