Question

Which one of the following statements is not a tautology ?

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

Answer 1

The correct option is C $(p\vee q)\to (p\vee (\sim q\left)\right)$

$$\begin{array}{cccccc}p& q& \sim q& p\vee q& p\vee \sim q& p\vee q\to p\vee \sim q\\ T& T& F& T& T& T\\ T& F& T& T& T& T\\ F& T& F& T& F& F\\ F& F& T& F& T& T\end{array}$$
All the rows of last column is not $T$.
So, $(p\vee q)\to (p\vee (\sim q\left)\right)$ is not a tautology.