Question

Show that the statement $p\wedge (\sim q)\Rightarrow p$ is Tautology.

Answer 1

$p$	$q$	$\sim q$	$p\wedge (\sim q)$	$p\wedge (\sim q)⟹p$
$T$	$T$	$F$	$F$	$T$
$T$	$F$	$T$	$T$	$T$
$F$	$T$	$F$	$F$	$T$
$F$	$F$	$T$	$F$	$T$

Tautology always takes "True" as its truth value. From above table we can say that $p\wedge (\sim q)⟹p$ is a tautology.