Question

Statements $(p\to q)\leftrightarrow [\{(p\wedge \sim q)\wedge t\}\vee c]$ is

• A. Tautology
• B. Contradiction
• C. Neither tautology nor contradiction
• D. Can't say anything

Answer 1

The correct option is B Contradiction

$P$	$q$	$t$	$c$	$P\to q$	$\sim q$	$P\wedge \sim q$	$(P\wedge \sim q)\wedge t$	$\{(P\wedge \sim q)\wedge t\}\vee c$	$(P\to q)\leftrightarrow [\{(P\wedge \sim q)\wedge t\}\vee c]$
T	T	T	F	T	F	F	F	F	F
T	F	T	F	F	T	T	T	T	F
F	T	T	F	T	F	F	F	F	F
F	F	T	F	T	F	F	F	F	F

Here, $t$=Tautology

$c$=Contradiction

$T$=True

$F$=false

Since, all are F in $(P\to q)\leftrightarrow [\{(P\wedge \sim q)\wedge t\}\vee c]$.

So, the given statement is Contradiction.