Chapter 1.3, Problem 1E

Determine whether or not each of the following arguments is valid.

$\begin{array}{l}p\to \left(q\to r\right)\\ q\end{array}$

$p\to r$

$\begin{array}{l}p\to q\\ q\vee r\end{array}$

$r\to \left(\neg q\right)$

$\begin{array}{l}p\to q\\ r\to q\end{array}$

$r\to p$

$\begin{array}{l}p\to q\\ \left(q\vee \left(\neg r\right)\right)\to \left(p\wedge s\right)\end{array}$

$s\to \left(r\vee q\right)$

$\begin{array}{l}p\to \left(\neg q\right)\\ r\to q\\ r\end{array}$

$\neg p$

$\begin{array}{l}p\to \left(\neg q\right)\\ \left(\neg r\right)\to p\\ q\end{array}$

$r$