Question

Which of the following is a contradiction

• A. $(p \land q) \land \sim(p \vee q)$
• B. $p \vee (\sim p \land q)$
• C. $(p \Rightarrow q) \Rightarrow p$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

p	q	p∧q	p∨q	$\sim(p \vee q)$	$(p \land q)\mspace{6mu} \land \sim(p \vee q)$
T	T	T	T	F	F
T	F	F	T	F	F
F	T	F	T	F	F
F	F	F	F	T	F

∴ $(p \land q) \land (\sim(p \vee q))$ is a contradiction.