Check the validity of `"If I do not work, I sleep.
If I am worried, I will not sleep. Therefore, if I am worried I will work"

Answer

To check the validity of the argument "If I do not work, I sleep. If I am worried, I will not sleep. Therefore, if I am worried, I will work," we can analyze the statements logically.

### Step-by-Step Solution:

1. **Identify the Statements:**
- Let \( P \): I work.
- Let \( Q \): I sleep.
- Let \( R \): I am worried.

The statements can be expressed as:
- Statement 1: If I do not work, I sleep. (If \( \neg P \), then \( Q \)) → \( \neg P \rightarrow Q \)
- Statement 2: If I am worried, I will not sleep. (If \( R \), then \( \neg Q \)) → \( R \rightarrow \neg Q \)
- Conclusion: If I am worried, I will work. (If \( R \), then \( P \)) → \( R \rightarrow P \)

2. **Translate the Statements into Logical Form:**
- From Statement 1: \( \neg P \rightarrow Q \)
- From Statement 2: \( R \rightarrow \neg Q \)
- We need to show that \( R \rightarrow P \) is valid.

3. **Analyze the Statements:**
- From Statement 1, if I do not work (\( \neg P \)), then I sleep (\( Q \)).
- From Statement 2, if I am worried (\( R \)), then I will not sleep (\( \neg Q \)).

4. **Consider the Implications:**
- If I am worried (\( R \)), according to Statement 2, I will not sleep (\( \neg Q \)).
- If I do not work (\( \neg P \)), then I must sleep (\( Q \)) according to Statement 1.
- However, if I am worried, I cannot sleep (\( \neg Q \)), which creates a contradiction if I do not work.

5. **Derive the Conclusion:**
- Since being worried (\( R \)) leads to not sleeping (\( \neg Q \)), and not working (\( \neg P \)) leads to sleeping (\( Q \)), the only way to resolve this contradiction is to conclude that I must work (\( P \)) when I am worried (\( R \)).
- Therefore, if I am worried, I must work, which validates the conclusion \( R \rightarrow P \).

### Conclusion:
The argument is valid. If I am worried, I will work.