Let p and q be two propositions given by
p : I play cricket during the holidays.
q : I just sleep throughout the day.
Then, the compound statement ` p vv q` is

Options

A. If I play cricket during the holidays, I just sleep throughout the day
B. I play cricket during the holidays and just sleep throughout the day
C. I just sleep during the holidays and only if I play cricket during the holidays.
D. I play cricket during the holidays or I just sleep throughout the day.

Explanation

To solve the problem, we need to express the compound statement \( p \lor q \) (where \( \lor \) represents the logical disjunction, or "OR") in a clear and coherent manner using the given propositions.

1. **Identify the propositions**:
- Let \( p \): "I play cricket during the holidays."
- Let \( q \): "I just sleep throughout the day."

2. **Write the compound statement**:
- The compound statement \( p \lor q \) can be interpreted as "I play cricket during the holidays OR I just sleep throughout the day."

3. **Combine the statements**:
- Using the logical disjunction (OR), we combine the two propositions:
- "I play cricket during the holidays OR I just sleep throughout the day."

4. **Conclusion**:
- The final expression of the compound statement \( p \lor q \) is:
- "I play cricket during the holidays OR I just sleep throughout the day."