Question

The statement $p\wedge (q\iff r)$ is a

• A. tautology
• B. contradiction
• C. contingency
• D. logically equivalent to $x\vee (\sim x)$

Answer 1

The correct option is C contingency

$p$	$q$	$r$	$q\iff r$	$p\wedge (q\iff r)$
$T$	$F$	$F$	$T$	$T$
$T$	$F$	$T$	$F$	$F$
$T$	$T$	$F$	$F$	$F$
$T$	$T$	$T$	$T$	$T$
$F$	$F$	$F$	$T$	$F$
$F$	$F$	$T$	$F$	$F$
$F$	$T$	$F$	$F$	$F$
$F$	$T$	$T$	$T$	$F$

As we know. a statement that is neither a tautology nor a contradiction is called a contingency. Hence the given statement is contingency.