Question

Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is:

• A. P does not marry Q and X marries Y.
• B. Neither P marries Q nor X marries Y.
• C. X does not marry Y and P marries Q.
• D. P marries Q and X marries Y.

Hint:

When negating a disjunction (OR), apply De Morgan's law to turn the disjunction into a conjunction (AND), and negate both parts of the statement.

Answer 1

The Correct Option is B

The given statement is a logical disjunction (OR statement) that says either \( P \) marries \( Q \), or \( X \) marries \( Y \). In symbolic logic, this can be written as: \[ P \text{ marries } Q \lor X \text{ marries } Y. \] To find the negation of this statement, we apply De Morgan's Law. De Morgan's law for negating a disjunction (\( A \lor B \)) states that the negation of this statement is equivalent to the conjunction of the negations of the individual components: \[ \neg (A \lor B) = \neg A \land \neg B. \] Thus, the negation of the original statement is: \[ \neg (P \text{ marries } Q \lor X \text{ marries } Y) = \neg (P \text{ marries } Q) \land \neg (X \text{ marries } Y). \] This means that both \( P \) does not marry \( Q \) and \( X \) does not marry \( Y \). In plain English, the correct negation of the statement is "Neither \( P \) marries \( Q \) nor \( X \) marries \( Y \)." This corresponds to option (B).
Final Answer: Neither \( P \) marries \( Q \) nor \( X \) marries \( Y \).