Question

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

• 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 the above

Hint:

De Morgan's law: $\sim(p \land q) = \sim p \lor \sim q$.

Answer 1

The Correct Option is B

To find the negation of the statement "Paris is in France and London is in England", we need to apply the principles of logical negation.

The original statement is:
\(A \land B\), where:
\(A:\) "Paris is in France"
\(B:\) "London is in England"

According to logical rules, the negation of a conjunction (\(A \land B\)) is the disjunction of the negations:

The negation is:
\(\neg (A \land B) \equiv \neg A \lor \neg B\)

Breaking it down:
- \(\neg A:\) "Paris is not in France"
- \(\neg B:\) "London is not in England"

Thus, the negated statement is:
"Paris is not in France or London is not in England."

Now, let's review the given options:

1. Paris is in England and London is in France.
2. Paris is not in France or London is not in England.
3. Paris is in England or London is in France.
4. None of the above.

The correct negation which matches our derived statement is option 2: "Paris is not in France or London is not in England."

Therefore, the correct answer is option 2.