Consider the following propositions :
P : I take medicine , q : I can sleep
Then , the compound statement ` ~ p to ~ q` means

Options

A. If I do not take medicine, then I cannot sleep
B. If I do not take medicine, then I can sleep
C. I take medicine iff can sleep
D. I take medicine if I can sleep

Explanation

To solve the problem, we need to analyze the given propositions and the compound statement.

1. **Identify the propositions:**
- Let \( P \) represent "I take medicine."
- Let \( Q \) represent "I can sleep."

2. **Negate the propositions:**
- The negation of \( P \) (denoted as \( \sim P \)) is "I do not take medicine."
- The negation of \( Q \) (denoted as \( \sim Q \)) is "I do not sleep."

3. **Understand the compound statement:**
- The compound statement given is \( \sim P \to \sim Q \). This can be read as "If I do not take medicine, then I cannot sleep."

4. **Interpret the statement:**
- The statement \( \sim P \to \sim Q \) indicates a conditional relationship. It suggests that the lack of taking medicine (not taking medicine) leads to the inability to sleep (not being able to sleep).

5. **Conclusion:**
- Therefore, the compound statement \( \sim P \to \sim Q \) means "If I do not take medicine, then I cannot sleep."

### Final Answer:
The compound statement \( \sim P \to \sim Q \) means "If I do not take medicine, then I cannot sleep."