Question

Examine whether the following logical statement pattern is tautology, contradiction or contingency
$\left[\right(p\to q)\wedge q]\to p$

Answer 1

$p$	$q$	$p\to q$	$(p\to q)\wedge q$	$[p\to q)\wedge q]\to p$
$T$	$T$	$T$	$T$	$T$
$T$	$F$	$F$	$F$	$T$
$F$	$T$	$T$	$T$	$F$
$F$	$F$	$T$	$F$	$T$

Since the truth table contains neither all $T$ nor all $F$ is the last column.
$\therefore \left[\right(p\to q)\wedge q]\to p$ is a contingency.