Question

Which of the following statements is not a tautology?

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

Answer 1

The correct option is D $(p\vee q)\Rightarrow (p\vee (\sim q\left)\right)$

$\begin{array}{cccccccccccc}p& q& p\wedge q& p\vee q& \sim p& \sim q& (\sim p)\vee q& p\vee (\sim q)& p\wedge q\Rightarrow (\sim p)\vee q& (p\wedge q)\Rightarrow p& p\Rightarrow (p\vee q)& (p\vee q)\Rightarrow (p\vee (\sim q\left)\right)\\ T& T& T& T& F& F& T& T& T& T& T& T\\ T& F& F& T& F& T& F& T& T& T& T& T\\ F& T& F& T& T& F& T& F& T& T& T& F\\ F& F& F& F& T& T& T& T& T& T& T& T\end{array}$