If p: The sun has set, q: The moon has risen, then symbolically the statement 'The sun has not set or the moon has not risen' is written as

Options

A. `p ^^ ~q`
B. `~q vv p`
C. `~p ^^ q`
D. `~p vv ~q`

Answer

To solve the problem, we need to convert the statement "The sun has not set or the moon has not risen" into symbolic form using the given propositions.

1. **Identify the propositions**:
- Let \( p \): The sun has set.
- Let \( q \): The moon has risen.

2. **Negate the propositions**:
- "The sun has not set" can be represented as \( \neg p \) (the negation of \( p \)).
- "The moon has not risen" can be represented as \( \neg q \) (the negation of \( q \)).

3. **Combine the negated propositions**:
- The statement "The sun has not set or the moon has not risen" can be expressed using logical disjunction (OR), which is denoted by \( \lor \).
- Therefore, we can write the statement as:
\[ \neg p \lor \neg q \]

Thus, the symbolic representation of the statement "The sun has not set or the moon has not risen" is \( \neg p \lor \neg q \).