Question

Which of the following statement is a tautology?

• A. $(\sim q \land p) \land q$
• B. $(\sim q \land p) \land (p \land \sim p)$
• C. $(\sim q \land p) \lor (p \lor \sim p)$
• D. $(p \land q) \land (\sim (p \land q)$

Answer 1

Answer: (C)

$(\sim q \land p) \lor (p \lor \sim p)$

Answer 2

$∵$ $(\sim q \land p) \lor (p \lor \sim p)$
$=$ $(\sim q \land p) \lor t$ (t is tautology) $≡ t$

So, the correct option is (C): $(\sim q \land p) \lor (p \lor \sim p)$