Let p : 7 is not greater than 4 and q : Paris is in France
be two statements. Then, `~(p vv q)` is the statement

Options

A. 7 is greater than 4 or Paris is not in France.
B. 7 is not greater than 4 and Paris is not in France.
C. 7 is not greater than 4 and Paris is in France.
D. 7 is greater than 4 and Paris is not in France.

Answer

To solve the problem, we need to analyze the given statements and then apply the negation to the logical expression.

1. **Identify the Statements**:
- Let \( p \): "7 is not greater than 4".
- Let \( q \): "Paris is in France".

2. **Translate the Statements**:
- The statement \( p \) can be interpreted as: "7 is less than or equal to 4" (which is false).
- The statement \( q \) is true because Paris is indeed in France.

3. **Formulate the Logical Expression**:
- We need to find the negation of the disjunction (logical OR) of \( p \) and \( q \), which is represented as \( \sim (p \lor q) \).

4. **Apply De Morgan's Law**:
- According to De Morgan's Laws, the negation of a disjunction can be expressed as the conjunction (logical AND) of the negations:
\[ \sim (p \lor q) = \sim p \land \sim q \]

5. **Negate Each Statement**:
- Negate \( p \):
- \( \sim p \): "7 is greater than 4" (which is true).
- Negate \( q \):
- \( \sim q \): "Paris is not in France" (which is false).

6. **Combine the Negated Statements**:
- Now, we combine the negated statements using logical AND:
\[ \sim (p \lor q) = \sim p \land \sim q \]
- This translates to: "7 is greater than 4 AND Paris is not in France".

7. **Final Statement**:
- Therefore, the final statement is: "7 is greater than 4 AND Paris is not in France".

### Summary of the Solution:
The statement \( \sim (p \lor q) \) translates to: "7 is greater than 4 AND Paris is not in France".