Question

If $p$ is true, $q$ is false and $r$ is false, then which of the following is true?

• A. $(p\vee q)\Rightarrow r$
• B. $p\wedge \sim (q\vee r)$
• C. $(p\vee q)\wedge r$
• D. $p\Rightarrow \sim (q\Rightarrow r)$

Answer 1

The correct option is B $p\wedge \sim (q\vee r)$

$p=T,q=F,r=F$

$\begin{array}{cccccccccc}p& q& r& p\vee q& \sim (q\vee r)& q\Rightarrow r& (p\vee q)\Rightarrow r& p\wedge \sim (q\vee r)& (p\vee q)\wedge r& p\Rightarrow \sim (q\Rightarrow r)\\ T& F& F& T& T& T& F& T& F& F\end{array}$