Negation of 'Paris is in France and London is in England' is

Options

A. Paris is in England and London is in France
B. Paris is not in France or london is not in England
C. Paris Is in england or london is in France
D. None of these

Explanation

To find the negation of the statement "Paris is in France and London is in England," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Statements**:
- Let \( P \): "Paris is in France"
- Let \( Q \): "London is in England"

2. **Combine the Statements**:
- The original statement can be expressed as \( P \land Q \) (P and Q).

3. **Apply De Morgan's Law**:
- According to De Morgan's Law, the negation of a conjunction (AND) can be expressed as the disjunction (OR) of the negations:
\[ \neg(P \land Q) = \neg P \lor \neg Q \]

4. **Negate Each Statement**:
- Negate \( P \):
- \( \neg P \): "Paris is not in France"
- Negate \( Q \):
- \( \neg Q \): "London is not in England"

5. **Combine the Negated Statements**:
- Using the results from the negations, we can express the negation of the original statement:
\[ \neg(P \land Q) = \neg P \lor \neg Q = \text{"Paris is not in France or London is not in England"} \]

6. **Match with Given Options**:
- Now, we check the options provided:
- Option 1: "Paris is in England and London is in France" (not a match)
- Option 2: "Paris is not in France or London is not in England" (this matches)
- Option 3: "Paris is in England or London is in France" (not a match)
- Option 4: "None of these" (not applicable)

7. **Conclusion**:
- The correct negation of the statement "Paris is in France and London is in England" is:
\[ \text{"Paris is not in France or London is not in England"} \]

### Final Answer:
The negation is: "Paris is not in France or London is not in England."

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