Question

What is the negation statement of the statement “Paris is in France and London is in England.”?
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

Answer 1

Hint: Use the definition of the negation in mathematical logic and get the negation statement of the given statement.

Formula Used:
The negation of a statement is the opposite of the original statement.
The negation is represented by a symbol: \[\sim\]

Complete step by step solution:
The given logical statement is “Paris is in France and London is in England.”
Let consider,
\[p:\] Paris is in France
\[q:\] London is in England
The symbolic representation of the given statement is: \[p \wedge q\]
Now apply the definition of a negation statement.
Then the negation representation is:
\[\sim \left( {p \wedge q} \right) = \sim p \vee \sim q\]
Therefore, the negation statement is,
Paris is not in France or London is not in England.

Hence the correct option is B.

Note: Students often get confused between the negation statement and the contrapositive statement in mathematical logic.
For contrapositive:
Original Statement: \[a \to b\]
Contrapositive statement: \[\sim b \to \sim a\]

For Negation:
Original Statement: \[a \wedge b\]
Negation statement: \[\sim a \vee \sim b\]