Question

The statement $p\wedge (\sim q\vee r)\vee (\sim r\vee q)$ is

• A. a tautology
• B. a contradiction
• C. logically equivalent to $x\vee (\sim x)$
• D. neither a tautology nor a contradiction

Answer 1

The correct option is D neither a tautology nor a contradiction

$\begin{array}{ccccccc}q& r& \sim q& \sim r& \sim q\vee r=x& y=\sim r\vee q& x\vee y\\ T& T& F& F& T& T& T\\ T& F& F& T& F& T& T\\ F& T& T& F& T& F& T\\ F& F& T& T& T& T& T\end{array}$

Now, $p\wedge (\sim q\vee r)\vee (\sim r\vee q)=p\wedge T=p$, which is neither a tautology nor contradiction.
$[\because (\sim q\vee r)\vee (\sim r\vee q)=x\vee y\text{is a tautology}]$