Chapter 1.1, Problem 29E

To determine

(a)

Use a truth table to show, $\left(p\uparrow q\right)\uparrow \left(p\uparrow q\right)$ is logically equivalent to $p\wedge q$.

To determine

(b)

Use a truth table to show, $\left(p\uparrow p\right)\uparrow \left(q\uparrow q\right)$ is logically equivalent to $p\vee q$.

To determine

(c)

Use a truth table to show, $p\uparrow \left(q\uparrow q\right)$ is logically equivalent to $p\to q$.