<p>The statement \(\sim(p \leftrightarrow \sim q)\) is</p>
Step-by-Step Solution
Key Concept: The biconditional p ↔ ~q is true when p and ~q have the same truth value. Its negation ~(p ↔ ~q) is true when p and ~q have different truth values, which means p and q have the same truth value.
<p><strong>Step 1:</strong> Recall that p ↔ q is true when both have the same truth value, false when they differ.</p><p><strong>Step 2:</strong> So p ↔ ~q is true when p and ~q have the same truth value (i.e., when p is true and q is false, or p is false and q is true).</p><p><strong>Step 3:</strong> Therefore ~(p ↔ ~q) is true when p ↔ ~q is false, which happens when p and ~q have different truth values.</p><p><strong>Step 4:</strong> This means p and q must have the SAME truth value, so ~(p ↔ ~q) is equivalent to (p ↔ q) or equivalently (p ∧ q) ∨ (~p ∧ ~q).</p><p>∴ Answer: A</p>
Correct Answer: A