Question

The proposition \( \neg (p \iff q) \) is equivalent to

• A. \( (p \vee \neg q) \land (q \vee \neg p) \)
• B. \( (p \vee q) \land (\neg p \vee \neg q) \)
• C. \( (p \neg q) \lor (q \neg p) \)
• D. None of the above

Hint:

The logical equivalence of negating a biconditional is the disjunction of the negations of the components.

Answer 1

The Correct Option is B

Step 1: Logical expression equivalency.
Using logical equivalencies, \( \neg (p \iff q) \) is equivalent to \( (p \vee q) \land (\neg p \vee \neg q) \).

Step 2: Conclusion.
The correct equivalence is \( (p \vee q) \land (\neg p \vee \neg q) \), corresponding to option (2).