Question

$[p\wedge (\sim q\left)\right]\wedge \left[\right(\sim p)\vee q]$

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

Answer 1

The correct option is B a contradiction

We know that,
$p\wedge (\sim q)\equiv \sim (p\Rightarrow q),$
$(\sim p\vee q)\equiv p\Rightarrow q$

Hence $[p\wedge (\sim q\left)\right]\wedge \left[\right(\sim p)\vee q]$ is a contradiction.
Since we know $x\wedge (\sim x)$ is always false.