<p>\((p \wedge \sim q) \wedge (\sim p \wedge q)\) is</p>
Step-by-Step Solution
Key Concept: A conjunction of two contradictory statements (p∧¬q) and (¬p∧q) can never both be true simultaneously, making the entire expression always false regardless of truth values of p and q.
<p><strong>Step 1:</strong> Analyze the structure: (p ∧ ¬q) ∧ (¬p ∧ q)</p><p><strong>Step 2:</strong> For this expression to be true, we need simultaneously: p is true AND q is false (from first part) AND p is false AND q is true (from second part).</p><p><strong>Step 3:</strong> This is impossible! We cannot have p both true and false at the same time. Similarly, q cannot be both true and false simultaneously.</p><p><strong>Step 4:</strong> Since no assignment of truth values to p and q can make this statement true, the expression is a <strong>Contradiction</strong> (always false).</p><p>∴ Answer: B (Contradiction)</p>
Correct Answer: B