Chapter 1.6, Problem 1E

In Exercises $1-7$, use a truth table to show that the given argument form (listed in Figure 1.70) is valid.

Modus Tollens.

Name	Abbreviation	Form
Modus Ponens	M. P.	$\begin{array}{l}p\to q\\ p\\ \therefore q\end{array}$
Modus Tollens	M. T.	$\begin{array}{l}p\to q\\ \sim q\\ \therefore \sim p\end{array}$
Hypothetical Syllogism	H. S.	$\begin{array}{l}p\to q\\ q\to r\\ \therefore p\to r\end{array}$
Disjunctive Syllogism	D. S.	$\begin{array}{l}p\vee q\\ \sim p\\ \therefore q\end{array}$
Constructive Dilemma	C. D.	$\begin{array}{l}\left(p\to q\right)\wedge \left(r\to s\right)\\ p\vee r\\ \therefore q\vee s\end{array}$
Absorption	Abs.	$\begin{array}{l}p\to q\\ \therefore p\to \left(p\wedge q\right)\end{array}$
Simplification	Simp.	$\begin{array}{l}p\wedge q\\ \therefore p\end{array}$
Conjunction	Conj	$\begin{array}{l}p\\ q\\ \therefore p\wedge q\end{array}$
Addition	Add.	$\begin{array}{l}p\\ \therefore p\vee q\end{array}$