Question

Which of the following statement pattern is a tautology ?

• A. $q\vee (q\to p)$
• B. $\sim q\to \sim p$
• C. $(q\to p)\vee (\sim p\leftrightarrow q)$
• D. $p\wedge \sim p$

Answer 1

Answer: (C)

(A) $p\vee (q\to p)\equiv p\vee (\sim q\vee p)\equiv p\vee p\vee \sim q$
$\equiv pv\sim q$
(B) $\sim q\to \sim p\equiv qv\sim p$
(D) $p\wedge \sim p\equiv F$
So left is (C)

$P$	$Q$	$q\to p$	$\sim p$	$\sim p\leftrightarrow q$	$(q\to p)\vee (\sim p\leftrightarrow q)$
T	T	T	F	F	T
T	F	T	F	T	T
F	T	F	T	T	T
F	F	T	T	F	T