Question

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency.
$(p\wedge \sim q)\leftrightarrow (p\to q)$

Answer 1

The given statement pattern is
$(p\wedge \sim q)\leftrightarrow (p\to q)$
Truth Table

$p$	$q$	$\sim q$	$p\wedge \sim q$	$p\to q$	$(p\wedge \sim q)\leftrightarrow (p\to q)$
$T$	$T$	$F$	$F$	$T$	$F$
$T$	$F$	$T$	$T$	$F$	$F$
$F$	$T$	$F$	$F$	$T$	$F$
$F$	$F$	$T$	$F$	$T$	$F$

All the entries in the last column of the above truth table are $F$.
$\therefore (p\wedge \sim q)\leftrightarrow (p\to q)$ is a contradiction.