Question

$(p\wedge ~q)\vee (~p\vee q)$is

• A. a contradiction
• B. a tautology
• C. either a or b
• D. neither a nor b

Answer 1

The correct option is A

a contradiction

Explanation for the correct option:

Checj=k if the relationship is a contradiction or tautology or both or neither of them:

We make a truth table to find the answer where $T$ denotes true and $F$ denoted false

$p$	$q$	$~p$	$~q$	$(p\wedge ~q)$	$~p\vee q$	$\left(p\wedge ~q\right)\wedge \left(~p\vee q\right)$
$T$	$T$	$F$	$F$	$F$	$T$	$F$
$T$	$F$	$F$	$T$	$T$	$F$	$F$
$F$	$T$	$T$	$F$	$F$	$T$	$F$
$F$	$F$	$T$	$T$	$F$	$T$	$F$

The last column has all $F$ which stands for false hence it is a contradiction.

Therefore the correct answer is option (A).