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

Options

A. Paris is in Engiand and London is in Drance
B. Paris is not in France or London is not in England
C. Parise is in England or London is in France
D. Paris is not in Fraince and London is not in England

Answer

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 \( P \) represent the statement "Paris is in France" and \( Q \) represent the statement "London is in England."

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

3. **Apply the Negation**:
The negation of \( P \land Q \) is given by De Morgan's Laws, which state that:
\[ \neg (P \land Q) \equiv \neg P \lor \neg Q \]
This means that the negation of "P and Q" is equivalent to "not P or not Q."

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

5. **Combine the Negated Statements**:
Using the OR operator, we can write the negation as:
\[ \neg P \lor \neg Q \]
In sentence form, this translates to:
"Paris is not in France or London is not in England."

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

---