Question

$(p \wedge \sim q) \wedge ( \sim p \wedge q)$ is

• A. tautology
• B. a contradiction
• C. both a tautology and a contradiction
• D. neither a tautology nor a contradiction

Answer 1

Answer: (B)

$( p \wedge \sim q) \wedge ( \sim p \wedge q)$
= $( p \wedge \sim p) \wedge ( \sim q \wedge q) $
= $f \wedge f = f$
(By using associative laws and commutative laws).
$\therefore \, (p \wedge \sim q) \wedge ( \sim p \wedge q)$ is a contradiction
$\therefore $ a contradiction holds