Question

The statement $(p\to (q\to p\left)\right)\to (p\to (p\vee q\left)\right)$ is :

• A. equivalent to $(p\vee q)\wedge (\sim p)$
• B. equivalent to $(p\wedge q)\vee (\sim p)$
• C. a contradiction
• D. a tautology

Answer 1

The correct option is D a tautology

$\begin{array}{ccccccc}p& q& q\to p& p\to (q\to p)& p\vee q& p\to (p\vee q)& (p\to (q\to p))\to (p\to (p\vee q))\\ T& T& T& T& T& T& T\\ T& F& T& T& T& T& T\\ F& T& F& T& T& T& T\\ F& F& T& T& F& T& T\end{array}$

Hence, the statement $(p\to (q\to p\left)\right)\to (p\to (p\vee q\left)\right)$ is a tautology.